What is the meaning of “knowledge and vision” in the context of the heartwood sutta?

Heartwood Sutta is one of the many suttas that paint the overall Path in broad strokes. We use these suttas to understand the elements of the Path from their relations to each other.

In this case the point of the sutta is to drive home the last step of the Path, cetto-vimukti, i.e. "liberation of mind" (or heart) as the only reliable differentiator between the Knowledge-and-Vision and all kinds of lesser knowledges, as superior to even this Knowledge-and-Vision, and as the only true Nirvana. The knowledge-and-vision (also described as "wisdom" in oher suttas) plays the role of the instrument or the gateway to Liberation.

Before I answer your question about the nature of Knowledge-and-vision I'd like you to first understand what Liberation actually refers to. This topic is not studied deeply in Theravada but is very well covered in Mahayana, especially in the live teacher-to-student traditions of Zen and Vajrayana. Liberation is a big topic and I don't have room here to describe it in detail, but to boil it down to its essence it is when, having realized how things work, you are no longer bothered by anything. You have no fear, no hope, no hindrance in the mind. You don't ascribe intrinsic value to anything. And now that you see that nothing is more valuable than anything else, nothing bothers you. Subjectively it feels as if you are finally free to just be spontaneous and true to yourself. (But remember: at this point you're quite clear on how things work, so you are free but not stupid.) You no longer define yourself, you have no shape, and you are not anchored in any single mental framework. You are undefined and spontaneous. You are free to do anything you decide, or not do anything at all.

1: What precisely is meant by “knowledge and vision” in this context?

Now, knowledge-and-vision (jnana-dassana) is exactly that understanding of how things work that, both, gives you assurance that nothing is intrinsically more important than anything else, and at the same time gives you clear insight into how certain actions lead to certain results. Once again, this knowledge-and-vision is quite deep and has multiple facets that all come together as one thing only when you truly get it. Until then you have to necessarily approach it from multiple sides as if it were multiple things. One of such aspects is Emptiness. Emptiness is an umbrella term that stands for the huge body of realizations and implications that come from the basic insight that "everything is defined relatively to something else". Another aspect of knowledge-and-vision is the Three Marks of Existence, or the nature of dharma-flow. When you truly understand TMoE you understand Emptiness and vice-versa. Another aspect of knowledge-and-vision is insight into how samsara comes about, that is how the developing mind assembles its superficial impressions into a full-blown subjective reality. This is usually explained as Dependent Origination but there's more to it than the standard formula. Another aspect of knowledge-and-vision is direct insight into the mechanism of semiosis that powers your own mindstream. This insight is obtained from the practice of Four Formless Jhanas and is also connected with Emptiness. Finally, the practice of Four (Rupa) Jhanas gives the insight into Four Noble Truths: Dukkha, Craving, Cessation of Craving, and Suchness. I can't emphasize enough that all of these only seem to be distinct ideas, but when you really get them they are aspects of the whole that I like to label "how things work".

Now, to answer your other questions:

2: Why is concentration a prerequisite for “knowledge and vision”?

It's not as much "dumb" concentration (in and of itself) as it is being able to focus on these topics and spend some quality time with them, to fully understand their implications. Well, I have to correct myself: when it comes to jhana practice, concentration is quite literally concentration on your own mind. Again, it's not just mechanical "dumb" concentration, it is concentration governed by a very specific goal: reaching the ultimate "sign" (the end of semiosis) in case of formless jhana, and reaching the ultimate "suchness" (the end of dukkha) in case of rupa-jhanas.

Both types of concentration are needed so you can exhaustively understand and truly get to the bottom of things.

3: Why is “knowledge and vision” a prerequisite for perpetual liberation?

As I explained above, cetto-vimukti is liberation of heart (or mind) through wisdom. Until you clearly see that nothing is more important than anything else, and until you know for sure why that is the case, it's really quite impossible to be free. Hence wisdom being the prerequisite for liberation.

My best guess is that ... This is a complete guess on my part. Am I close?

No, not at all. Yours is a typical misunderstanding of the final stages of the Path. The liberation is not attained through watertight control of the mind. It's not a sterile state. It's a state of having transcended the boundaries of all those frameworks that kept you captive.