Secondly, can the right hand seat person log the hours as P2
Technically you can log it as your flying will be done on the basis of an FAA PPL and there is no requirement to have a separate logbook for FAA/JAA flying. Problem will be that the JAA will not allow it to be used for unfreezing of your license or any currency requirements.
You cant log P.2 in a single pilot ops certified aeroplane.
You can in FAA land. I don't make the rules. That's how the Average American Joe has twice as many hours as as