I don't know if my answers are 100% grammatically accurate, but this is how I think about them:
1) The na-adjectives also behave as nouns. To use them as adjectives you add な.
This is a clean room.
This room is clean.
In the second example きれい acts as a noun, so to say this is not a clean room you'd have
in the same way that you'd happily write 犬じゃない. So, I don't see this じゃ as a conjugation, rather, it's just part of the negative copula (じゃない). You could equally well write きれいではありません etc.
2) ます is a polite conjugation of a verb. です only adds to i-adjectives. It is not a conjugation of the adjective, it is just added on to the end to make the sentence more polite. For example:
are both equally good, just with different levels of politeness.
3) You need to clarify this question. I don't understand what you're asking. If I had to guess, maybe you're thinking about things like きれいではありません, in which case, refer to 1).
Edit: Still not quite sure what you mean. You seem to be asking about negating adjectives. For i-adjectives you change the final い to a く and then add the negative form of the verb ある on to the end. That gives you a formal and an informal way to write it:
Because ない itself behaves like an i-adjective the latter case can be made formal by adding です as discussed in 2):
For the past tense conjugate ある just like you would if it was a stand-alone verb:
4) Not quite sure what you mean, but I'm going to say that the answer is yes.
For an i-adjective you take of the final い and add かった:
おいしい -> おいしかった
For a na-adjective, as we discussed in 1), you conjugate the copula rather than the adjective:
きれいです -> きれいでした
5) I doubt it, but I'm not even remotely qualified to answer that question. It's an interesting question, but probably not so helpful to your studies at this stage.