You are right. I really can't tell if it's a stolen watch even if it comes with the paper. But the possiblity would be lower because normally thieves only search for watches and valuables. They don't bother about papers and box (I doubt whether they would take the papers even if the papers are put beside the watches in the vault). One thing we could do is to apply for an Archives paper to make sure it's not recorded stolen.
As for the second question, I think they would honour the warranty provided it's within the period. I have no such experience but I do think PP watches should be like other commodities (e.g. TV and cellphones). It's their job to provide services for the watches they sell and these watches can be traded in the grey market and they can also be gifts. Do you agree?