P3. I agree. Work back through any argument and you arrive at what's called absolute presuppositions. And these are just those ideas that are presupposed, in the sense that they're axiomatic for the argument (belief, understanding, conclusion, etc.).

C. I disagree. You do know the truth of the conclusion with respect to the structure of the argument, both in terms of form and content. Or in other words, in terms of the axioms or presuppositions.

Is the conclusion absolutely true? Not a meaningful question. Truth is relative to the criteria that establish it. You're sitting in a chair. Is it a chair? Of course it is. Unless you're a scientist of the very small, in which case what the "chair" is depends on the scale you're looking at it with. Or a Kantian, in which case you merely think of it as a chair, but really don't know what it is at all. And so forth.

The idea of truth being relative is really what I wanted someone to arrive at. Since P3 and P2 are true, that restricts all forms of philosophical enquiries to only being true based on certain presuppositions. Has anyone else ever noticed that whenever there is a real disagreement in philosophy, that most of the time it is the result of both sides taking different presuppositions to be true and that neither side actually has unltimate proof for his presuppositions? It is rarely the case that a philosophical disagreement (one that continues for a long time) is a result of a failure at applying the presuppositions of logic. And most of the time these disagreements are resolved is when someone synthesizes the irreconcilable presuppositions somehow. I find it infinitely easier to reach a conclusion in debates when you become aware of the other sides implicit presuppositions and you lay them out and examine them next to your own. The idea of every premise being doubtable (not saying practically) is extremely unnerving yet liberating at the same time. I'd like to see more answers to the 2 main questions.

1- Are there any more elementary presuppositions such as P1/2/3/4 that would sway the conclusion of this argument (for example, is there one premise that is completely undoubtable therefore making P3 false?)
2- Is there a way to do away with any of P1/2/3/4 (Is any of them false? Specifically, is there a way to show P2/3 is false?)

Pyrrhonean skeptics were so skeptical they didn't even have a stance on whether or not knowledge was possible. I'm trying to find good arguments for both cases in this thread

Right.
If knowledge acquisition is to be deductive, then we run into the diallelus (links below).
Knowledge acquisition in general isn't purely deductive, however, which means we'll need good standards of justification, perhaps something like evidence and reason together (starting out in that order).

Regress argument (Wikipedia)
The Problem of the Criterion (IEP)

This is not 'pyrrhonian scepticism' but sophistry. It misses the practical aim of Pyrrho and his ilk, which is to attain the state of imperturbability (ataraxia) by 'withholding judgement on what is not evident'.

Now there is quite a strong school of thought that Pyrrho got these ideas from Buddhism. He was alive during the reign of Alexander the Great, whose kingdom extended East to Bactria and Gandhara, which is present day Afghanistan and Pakistan. These at the time were thriving centres of Mahayana Buddhism, and Pyrrho of Elis was said to have travelled there to engage in dialog with the Indian 'gymnosophists' (i.e. ascetic philosophers.)

There's been a lot written on this theme, with one of the seminal papers being Pyrrho and India, Edward Flintoff; also Pyrrhonism: How the Ancient Greeks Reinvented Buddhism (Studies in Comparative Philosophy and Religion), Adrian Kuzminski, http://a.co/d/dCobqIm , and Sunyata and Epoché by Jay Garfield (the latter showing how the idea of 'suspension of judgement' or Epoché was used by Husserl in the establishment of phenomenology, which is one of the factors that has lead to a recent confluence of Buddhism and phenomenology in cognitive science and philosophy (e.g. here.)

That is the only thing that is interesting about it to me. The interminable arguments about 'what is a true proposition' on philosophy forums are a hamster wheel.