Which seat you're in is irrelevant. You can fly solo from the right seat if you want as P1.
As has been said above, you can only log P2 in a multi crew aircraft.
I think you can only fly from the right hand seat if the left is occupied. The left hand seat person does not even have to be a PPL holder. If you are solo, I have been told that you have to sit in the left hand seat?????????????
Can anyone confirm this