I think this was covered in the document In Abbas Ortus ex Silenti, in which it was definitively stated that he’d be given a minute or two to catch his breath and have a glass of water first. So, no, not immediately.
The current Pope has all the authority Peter had when alive, so, no, Peter would not be Pope if he somehow came back to life. Although I’m sure the Pope would be very interested to know WHY Peter was ‘back’!
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