This is irrelevant to the validity of the argument and the truth of the conclusion. Since '~P → P' is--in an important sense--just another way of writing 'P', of course, if '~P' is true, then 'P' is false and we have contradicted the premise, but '~P' is neither a premise nor entailed '~P → P'. In other words, '~P → P' does not contradict 'P v ~P', and so it's irrelevant except as a means to construct an unnecessarily complicated proof.
It's not an "unnecessarily complicated proof", it is a non-abbreviated proof, which does not hide the RAA needed for the complete logic when law of noncontradiction and excluded middle are taken into account.
If you want to construct a reductio ad absurdum, then yes, both formulae are used to deduce 'P & ~P'. However, while assumptions must be discharged for the deduction to be valid, premises need not be. In fact, the rule is customarily that premises are never discharged. Since 'P' is the only premise, then, only '~P' can be discharged by the reductio ad absurdum.
Yes, but if you arbitrarily favor a premise like that, it still requires a RAA after the aforementioned laws are applied. RAA would discharge the assumption instead, and without the assumption the conclusion is not valid.
I was just trying to get across why such a definition of Identity would be used when I said the premise would be equally worthy of discharge, not making a formal logical statement. As I said, if Identity doesn't include those two laws, then it's an Identity (the premises and conclusion entail each other either way).