For 1) the answer is basically to figure out what bets you're willing to make. You don't know anything, for strong definitions of know. Absolutely nothing, not one single thing, and there is no possible way to prove anything without already knowing something. But here's the catch; beliefs are probabilities. You can say "I don't know that I'm not going to be burned at the stake for writing on Less Wrong" while also saying "but I probably won't be". You have to make a decision; choose your priors. You can pick ones at random, or you can pick ones that seem like they work to accomplish your real goals in the real world; I can't technically fault you for priors, but then again justification to other humans isn't really the point. I'm not sure how exactly Coherentists think they can arrive at any beliefs whatsoever without taking some arbitrary ones to start with, and I'm not sure how anyone thinks that any beliefs are "self-evident". You can choose whatever priors you want, I guess, but if you choose any really weird ones let me know, because I'd like to make some bets with you... We live in a low-entropy universe; simple explanations exist. You can dispute how I know that, but if you truly believed any differently then you should be making bets left and right and winning against anyone who thought something silly like that a coin would stay 50/50 just because it usually does. Basically, you can't argue anything to an ideal philosopher of perfect emptiness, any more than you can argue anything to a rock. If you refuse to accept anything, then you can go do whatever you want (or perhaps you can't, since you don't know what you want), and I'll get on with the whole living thing over here. You should read "The Simple Truth"; it's a nice exploration of some of these ideas. You can't justify knowledge, at all, and there's no difference between claiming an arbitrary set of axioms and an arbitrary set of starting beliefs (they are literally the same thing), but you can still count sheep, if you really want to. 2) is mostly contained in 1), I think.
3) Why do you need empirical evidence? What could that possibly show you? I guess you could theoretically get a bunch of Contextualista and Invariantists together and show that most of them think that "know" has a fundamental meaning, but that's only evidence that those people are silly. Words are not special. To draw from your lower comment to me, "a trout is a type of fish" is not fundamentally true, linguistically or otherwise. It is true when you, as an English speaker, say it in an English forum, read by English speakers. Is "Фольре є омдни з дівви риб" a linguistic truth? That's (probably) the same sentence in a language picked at random off Google Translate. So, is it true? Answer before you continue reading. Actually, I lied. That sentence is gibberish; I moved the letters around. A native speaker of that language would have told you it was clearly not true. But you had no idea whether it was or wasn't; you don't speak that language, and for that matter neither do I. I could have just written profanity for all I know. But the meanings are not fundamental to the little squiggles on your computer screen; they are in your mind. Words are just mental paintbrush handles, and with them we can draw pictures in each other's minds, similar to those in our own. If you knew that I had had some kind of neurological malfunction such that I associated the word "trout" to a mental image of a moderately sized land-bound mammal, and I said "a trout is a type of fish", you would know that I was wrong (and possibly confused about what fish were). If you told me "a trout is a type of fish", without clarifying that your idea of trout was different from mine, you'd be lying. Words do not have meanings; they are simply convenient mental handles to paint broad pictures in each other's minds. "Know" is exactly the same way. There is no true, really real more real than that other one meaning of "know", just the broad pictures that the word can paint in minds. The only reason anyone argues over definitions is to sneak in underhanded connotations (or, potentially, to demand that they not be brought in). There is no argument. Whatever the Contextualists wants to mean by "know" can be called "to flozzlebait", and whatever the Invariantists wants to mean by it can be called "to mankieinate". There, now that they both understand each other, they can resolve their argument... If there ever even was one (which I doubt).
1: The Foundationalists have claimed probability is off the metaphorical table- the concept of probability rests either on subjective feeling (irrational) or on empirical evidence(circular, as our belief in empirical evidence rests on the assumption it is probable). They had problems with self-evident, but I created a new definition as "Must be true in any possible universe" (although I'm not sure of the truth of his conclusion, the way EliIizer describes a non-reductionist universe basically claims for reductionism this sort of self-evidency).
2...
I have naturally read the material here, but am still not sure how to act on two questions.
1: I've been arguing out the question of Foundationalism v.s Coherentism v.s other similiarly basic methods of justifying knowledge (e.g. infinitism, pragmatism). The discussion left off with two problems for Foundationalism.
a: The Evil Demon argument, particularly the problem of memory. When following any piece of reason, an Evil Demon could theoretically fool my reason into thinking that it had reasoned correctly when it hadn't, or fool my memory into thinking I'd reasoned properly before with reasoning I'd never done. Since a Foundationalist either is a weak Foundationalist (and runs into severe problems) or must discard all but self-evident and incorrigible assumptions (of which memory is not one), I'm stuffed.
(Then again, it has been argued, if a Coherentist were decieved by an evil demon they could be decieved into thinking data coheres when it doesn't. Since their belief rests upon the assumption that their beliefs cohere, should they not discard if they can't know if it coheres or not? The seems to cohere formulation has it's own problem)
b: Even if that's discarded, there is still the problem of how Strong Foundationalist beliefs are justified within a Strong Foundationalist system. Strong Foundationalism is neither self-evident nor incorrigible, after all.
I know myself well enough to know I have an unusually strong (even for a non-rationalist) irrational emotive bias in favour of Foundationalism, and even I begin to suspect I've lost the argument (though some people arguing on my side would disagree). Just to confirm, though- have I lost? What should I do now, either way?
2: What to say on the question of skepticism (on which so far I've technically said nothing)? If I remember correctly Elizier has spoken of philosophy as how to act in the world, but I'm arguing with somebody who maintains as an axiom that the purpose of Philosophy is to find truth, whether useful or useless, in whatever area is under discussion.
3: Finally, how do I speak intelligently on the Contextualist v.s Invariantist problem? I can see in basic that it is an empirical problem and therefore not part of abstract philosophy, but that isn't the same thing as having an answer. It would be good to know where to look up enough neuroscience to at least make an intelligent contribution to the discussion.