Thank you for your questions. Whilst they spur one to pause for thought, their subject matters aren't quite attuned to the purely metaphysical issues posed by theories of truth. Allow me to demonstrate.
Firstly, your epistemic questions. If we spent our lives in sensory deprivation, there would still in principle be plenty of knowable facts, and thereby plenty of propositions we could identify as true. Basic mathematical principles and axioms of simple logics would be examples of such. Recall, if you will, Russell's explicit avowal of such things as arithmetical facts to contrast with physiological ones. Now, there would certainly be some facts that would be unknowable if we had no sensory access to anything, but what we could know would still suffice to grasp adequate conceptions of propositionality, of facthood and of correspondence. That twice two is four would be an example of a fact to which a the proposition "two plus two equals four" would correspond, and conversely the proposition "two plus two is seven" would illuminate a failure of correspondence. If you require examples of knowable contingent propositions, cases abound:
that one is aware of the Russell paradox, or of the relation between a natural logarithm and its integral, or of that between an imaginary number and its square,
et cetera. Cases of self-knowledge are, for us mortals, metaphysically contingent.
Even if, contra platonism, mathematical objects are mental constructs, the picture of facts and propositions the correspondence theorist requires remains intact. All that would change is that facts about mathematics and its kin would become facts about our internal mental entities and phenomena. We would still have something for a proposition to correspond to, much like how a subjectivist of value theory still considers there to be truthmakers to evaluative sentences.
All this holds for other theories of truth aside the correspondence theory,
mutatis mutandis. The maxim,
p is true iff ___ would still be retained without the blank being forcibly substituted. Because truth theorists aren't interested in
which truths are knowable, scepticism of an external world only forces such theorists to restrict the examples they give, and nothing more.
Now for your modal question. You ask how there can be a correspondence relation between a proposition and something that doesn't exist. My answer is clarificatory remark. When we declare that
p is metaphysically possible, we are not making a claim about the
truth of
p but of the possible truth thereof. A correspondence theorist can happily accept that possible truth is a correspondence between a proposition and a non-obtaining state of affairs, for this doesn't impinge upon her answer to what truth consists of, or more precisely but redundantly, what
actual truth consists of. Note that this is separate to the question of how a modal statement can be (actually) true under a correspondence theory, as opposed to how a non-modal statement can be possibly true. Answering the former question is, alas, quite a lengthy matter, as it is not neutral with respect to one's views on possible worlds.
Your question of what reality consists of according to a modal realist may be addressed by appealing to the most lucid of sources on the matter.
David Lewis wrote:Nor does this world differ from the others in its manner of existing. I do not have the slightest idea what a difference in manner of existing is supposed to be. Some things exist here on earth, other things exist extraterrestrially, perhaps some exist no place in particular; but that is no difference in manner of existing, merely a difference in location or lack of it between things that exist. Likewise some things exist here at our world, others exist at other worlds; again, I take this to be a difference between things that exist, not a difference in their existing. You might say that strictly speaking, only this-worldly things really exist; and I am ready enough to agree, but on my view this 'strict' speaking is restricted speaking, on a par with saying that all the beer is in the fridge and ignoring most of all the beer there is. When we quantify over less than all there is, we leave out things that (unrestrictedly speaking) exist simpliciter. If I am right, other-worldy things exist simpliciter, though often it is very sensible to ignore them and quantify restrictedly over our worldmates. (On the Plurality of Worlds, pp.2-3, italics are Lewis'.)
Under this sort of framework, the truth predicate could be rephrased as
true-at-our-world, and the possible truth predicate as
true at some world. Likewise, an obtaining state of affairs could be qualified as a state of affairs that obtains at the world of discourse, as opposed to possible states of affairs that obtain elsewhere.
Wittgenstein's early use of pictures was for linguistic purposes. Pictures are certainly representations of things which possess
pictorial forms within themselves and which that share a
logical form with the worldly states of affairs they represent, but they are not essentially
cognitive. This is to say nothing of his theory's problems though.
Your penultimate question lacks force. I do grant that the correspondence theory might be false for reasons we have not yet discussed. (Indeed, I prefer a deflationary theory of truth.) Now, for me to doubt whether the correspondence theory is
true is perfectly permissible, as there's no general problem with employing a certain concept in an assessment of an analysis of that concept itself. A sceptical utilitarian can doubt whether utility is the good without considering something problematic or meaningless, contra Moore, and likewise a truth theorist can wonder whether our conception of truth is fully served by the biconditional she advocates as an analysis thereof. That we can doubt the suitability of an analysis doesn't change the consequences of such an analysis itself, independently of our endorsement thereof.
Regarding your final question I have this to say. Under the correspondence theory we must assert that
 \leftrightarrow \exists y(Fact(y)\wedge Corresponds(x,y))))
. Let us call this proposition

. You are right to hold that given this, we must assert that
\wedge Corresponds(P,z)))
, which we might identify as proposition

, and thus assert that
\wedge Corresponds(Q,\alpha)))
and so on. I think, in such cases, that the aforementioned "Great Fact" can easily be identified with all of the facts from

and

onwards that this process requires. To illuminate, consider how if there is a fact corresponding to "it is true that
p", there needn't be any other facts, save those regarding the meaning of the relevant terms, for "it is true that 'it is true that
p'" to
eo ipso be true, and so on for iterative embeddings. A regress is only apparent.