The answer to these two questions is "That depends!" Firstly, it depends on the kind of knowledge that is being discussed. And secondly, it depends on the theory of knowledge that is brought to the meaning of "reasons". I will address first the various theories of what knowledge is, and whether "having good reasons for one's beliefs" is meaningful within these theories. I will leave the question of what might constitute "good reasons" until I have identified some theories that involve one having good reasons for one's beliefs.
Not all kinds of knowledge are the kind that would be normally expected to involve reasons and beliefs. Philosophers recognize three different kinds of knowledge -- familiarity (knowledge of), ability (knowledge how), and propositional (knowledge that). It is propositional knowledge that is considered to be the kind of knowledge for which beliefs and reasons are defining characteristics. Beliefs and reasons are spoken of in connection with the first two of these kinds of knowledge, but it is generally considered to be allegorical attribution. Familiarity knowledge and ability knowledge as normally conceived are not considered to be the kind of knowledge that involves beliefs and reasons. So it is safe to assume that the title question is addressed specifically to propositional knowledge.
Philosophers have offered different kinds of theories as to just what propositional knowledge is -- theories that would give different meaning to the concept of a reason for one's beliefs. There are some theories of knowledge that would deny that knowledge is something that involves reasons, and some theories that would deny that knowledge involves beliefs.
The performative theory of knowledge, for example, regards the verb "know" as in the same category as such verbs as promise, warn, order, etc. To know is to do something. To know is to give an assurance or warrant. Knowledge, on this theory, is not something that involves having reasons. Hence, from such a theory of propositional knowledge, because having knowledge is a performative act and not an epistemic status, knowledge does not involve having good reasons for one's beliefs. And the question of what constitutes "good reasons" is therefore moot.
Some theories of knowledge recognize two different kinds of propositional knowledge -- intellectual or reflective and animal or non-reflective. Intellectual propositional knowledge is normally considered a true belief that is justified with sufficiently supportive evidence or intellectually drawn inferences -- reasons -- of either the deductive, inductive, or abductive kind. Animal or non-reflective propositional knowledge, by comparison, is a true belief that is arrived at through some reliable non-intellectual process. It is the kind of propositional knowledge that can be attributed to animals and pre-intellectual children, and obtained quickly without intellectual effort, when time is too short for reflective development of reasons (as in moments of crisis). Because animal knowledge is not obtained through intellectual processes, it does not involve having reasons. Hence, if the title question is addressed specifically to "animal knowledge", then the answer would have to be -- " No! (Animal) Knowledge does not involve having good reasons for one's beliefs." But not all theories of knowledge recognize that "animal knowledge" is indeed a true form of propositional knowledge.
Because the title question speaks specifically about having reasons, I should make clear the first-person versus third-person sense of S being justified in (having reasons for) believing that P. The first-person sense is sometimes referred to as "personal justification", or "epistemic responsibility". The subject S, to be justified in this sense, must live up to certain epistemic standards of behaviour. For example, the subject must be aware of some evidence that suggests that P is more likely, and must not ignore any evidence that suggests that P is less likely. In the third-person sense, S is judged to be justified in believing that P if there exists enough supporting evidence that makes P more likely, and there does not exist any defeater evidence that makes P less likely. This sense is sometimes referred to as "general justification" or "epistemic grounding", meaning that there must be adequate grounding for a belief that P. The distinction is relevant here because all theories that admit that knowledge involves beliefs grant that there must be epistemic grounding (good reasons) for one's belief that P. But not all admit that knowledge involves having (being aware of) those good reasons.
The "diffident scholar" example has been proposed to argue that knowledge might not necessarily involve belief. The diffident scholar studies some subject thoroughly, and answers questions on that subject correctly -- say that the mass of the tau neutrino is 18.2 MeV. However, because of nerves or pressure, he does not believe that he knows the answer and thinks that he is only guessing. He does not believe that the mass of the tau neutrino is 18.2 MeV. He is merely picking from a multiple-choice list the answer that seems (more or less vaguely) the best. It is argued from this example that there are adequate grounds to claim he does know despite the missing belief. This is a third-person "epistemic grounding" focus on the question. This example highlights the distinction between the first and third person sense of having reasons for one's beliefs. And it suggests that there are two kinds of answers as to what constitutes "good reasons" for one's beliefs.
Theories of propositional knowledge can be divided according to whether they place their emphasis on the first-person "epistemic responsibility" sense of justification, or on the third-person "epistemic grounding" sense of justification. "Internalist" theories, like the Justified True Belief theories, focus on the "epistemic responsibility" sense of justification. An internalist would say that knowledge requires one to have good reasons for one's beliefs. (Of course, internalist theories of knowledge, because of their focus on intellectual justification, would consider animal or non-intellectual knowledge to be merely allegorical attribution.) "Externalist" theories, on the other hand, focus on the "epistemic grounding" sense of justification, often to point of excluding entirely the first person sense. While an externalist would agree that for knowledge there must be good reasons for one's beliefs, a pure externalist theory of knowledge would maintain that knowledge does not involve one having good reasons for one's beliefs.
Pure externalist theories of knowledge maintain that whether a belief is knowledge or not is dependent only on factors that are external to, and hence not necessarily known by, the subject. Thus, while good reasons are clearly necessary within such theories, they are not reasons that the subject necessarily is aware of. Pure reliablism, for example, demands only that a true belief be produced by a reliable process of some kind. The causal theory of knowledge demands that a true belief be suitably caused. Nozick's truth-tracking theory, as another example, demands that a true belief satisfy a pair of subjunctive counterfactual conditionals. To an externalist then, a "good reason" for one's belief would be that it is formed by some sort of reliable process, or caused in some suitable way by the facts of the matter, or satisfies Nozick's pair of subjunctive conditionals. But on none of these theories does knowledge involve one having good reasons for one's beliefs.
Only if one approaches the title questions from the perspective of an internalist theory (or possibly a "modified" - i.e. not pure - externalist theory) of propositional knowledge, will the issue of having good reasons for one's beliefs arise. The "Standard Model" for theories of knowledge, against which all alternative variations are compared (and constructed) is the "Justified True Belief" (JTB) theory of knowledge.
By definition, according to this standard model, the category of intellectual propositional knowledge does require one to have good reasons for one's beliefs. The question now arises -- just what are "good reasons".
Echoing the discussion above, within the family of JTB theories of knowledge, there are two different models of what constitutes "justification". The "prior grounding" model of justification demands that one be aware of (or at least have access to) the reasons that constitute one's justification in order to validly claim knowledge. This model assumes that the third-person epistemic grounding sense of justification has priority over the first-person or epistemic responsibility sense. A person fulfills his epistemic responsibility if he has gained adequate awareness of that grounding. The "good reasons" that one must have consist of the awareness of the various elements of the adequate epistemic grounding for the belief. We'll get into what those elements are in a moment.
The "default and challenge" model, on the other hand, grants default warrant to some beliefs unless challenged. It places the priority on epistemic responsibility. Epistemic grounding is involved only when, and to the extent that, a claim to knowledge is challenged. One does not necessarily have to have (be consciously aware of) the good reasons that exist for one's beliefs to qualify them as knowledge. The "good reasons" that one must have for one's beliefs consist of either (a) the awareness of the various elements of the adequate epistemic grounding for the belief; or (b) the awareness of an absence of challenges or defeaters for one's default claim to knowledge. Part of the necessary epistemic grounding might in fact be some externalist factor about which the subject could not be aware.
To understand just what might constitute "good reasons" from an epistemic grounding perspective, we have to delve a little deeper into some of the theories of justification. The two most popular of these are the theories of Foundationalism and Coherentism. In their more popular forms, both of these theories are strictly internalist, and adopt the "prior grounding" model of justification.
Foundationalism maintains that there are kinds of beliefs that are "self-justifying". Foundational beliefs are, by their very nature, true and self-presenting (i.e. self-justifying) simply in virtue of the fact that we have them. Perceptual beliefs are generally among the kinds of beliefs that are proposed as foundational. If one perceives that P (in some tightly constrained understanding of "perceive" ), then one is thereby justified in believing that P. Other beliefs are justified by being "based" (in some tightly constrained understanding of "based" ) on foundational beliefs. From the context of a Foundationalist theory, then, a "good reason" for one's beliefs would consist of either that belief being a foundational belief (for example a "perception" that P), or being suitably "based" on some foundational beliefs that make it more likely that P and/or less likely that not-P.
Coherentism, by contrast, does not grant to perceptual beliefs any special epistemic status. Coherentism maintains that beliefs are justified only if, and to the extent that, they "cohere" (in some tightly constrained understanding of "cohere" ) with the rest of what one believes. Justification is holistic rather than linear or hierarchical. From the context of Coherentism, then, a "good reason" for one's beliefs would consist of (1) the belief "coheres" with the rest of what one believes; and (2) whatever other beliefs in one's coherent set of beliefs make it more likely that P and/or less likely that not-P.
There is another, although less popular, of the JTB theories that resolves many of the challenges facing foundationalism and coherentism, while maintaining many of their desirable features. That theory is the Contextualist theory of knowledge (specifically the Inferential Contextualism of Williams). It is still a Justified True Belief theory. But it is not entirely internalist, because it incorporates some of the features of Reliablism. The key difference between Contextualism and the other theories is that it adopts the fallibilist "default and challenge" model of justification, and switches the priority of justification from the "prior grounding" conception to the "epistemic responsibility" conception. The basic principle of contextualism is that if it seems to S that P, then S is prima facie justified in believing that P.
Elements of coherentism show up in the "prima facie" (and in the attribution of meaning to propositions). It is necessary that the belief that P "cohere" with whatever other beliefs that one might have -- pretty much in the way that Coherentists would maintain, although only locally with beliefs that are contextually relevant rather than holistically with the entire suite of beliefs. Elements of foundationalism show up in the recognition that perceptual inputs have special epistemic status -- although that special status is generated contextually by one's epistemic beliefs rather than by some intrinsic (objective) property of foundational beliefs. Contextualism does not share foundationalism's difficulty with understanding the meaning of foundational propositions, because it understands perceptual awareness in a coherentist way -- perceptual awareness is wrapped by beliefs about word meanings and the meaning of conceptual categories.
According to contextualism, then, a "good reason" for one's belief that P is (prima facie) that one perceives that P. Equivalently, a "good reason" for me to believe that P is that it seems to me that P, when I have no reason to suspect that the way in which it seems to me might not be verdical. Alternatively, if one's belief is not of the "seeming" kind, then one can apply a modified version of the sort of normative standard that coherentism employs - a "good reason" for one's belief would consist of (1) the belief "coheres" with a relevant sub-set of what else one believes; and/or (2) whatever other beliefs within that relevant sub-set that make it more likely that P and/or less likely that not-P. Second order epistemic beliefs about the reliability of one's belief forming processes show up in the contextual coherence net of "good reasons" for one's beliefs. The fact that I believe my perceptions to be a reliable indicator of the truth of things, is a "good reason" for believing that (prima facie) things are as they perceptually appear.
According to contextualism, in claiming knowledge I am committed to the fact that my belief is adequately grounded, but my epistemic responsibility does not require me to have already confirmed its grounding. The epistemic grounding for my belief might consist of it being suitably caused, or formed via a reliable process. This aspect of contextualism draws in a lot of the benefits of Reliablist theories of knowledge, like its compatibility with evolutionary theory.
From the perspective of contextualism, then, knowledge does involve having "good reasons" for one's beliefs. And those good reasons would consist of -
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