What are the rules and regulations regarding letting him sit on the left hand side, whilst I fly as P1 on the right hand side?
So, to summarize, there are no specific rules that force the PIC to sit on the LHS. There may be specific rules in the POH ("solo from rear seat only" in a tandem seater for instance) but
AFAIK that doesn't apply to the PA28.
Obviously you need to have access to all the instruments, levers and such for the flight required. In case of the PA28, you will probably want to give the pax a thorough briefing on switching fuel tanks, and maybe (re)starting the engine (if the starter is out of your reach). And it may not be the best of ideas for an IFR flight (which this isn't) unless all instruments are duplicated.
Furthermore, it's not a bad idea to get some experience flying (and landing) from the RHS. The picture is different, you've got to swap hands and such. Not particularly difficult, but you'll want to be careful the first few times.
Also, I've flown this very aircraft as P2 on the right hand side
There's no such thing as a P2 in a PA28 since it's a single pilot aircraft. The only way two people can log time simultaneously in a PA28 is the instructor/student or examiner/student scenario. Unless you were involved in operations which, per company SOP, required a two-man crew. Which is very, very unlikely in a PA28.
Does the owner allow it?
Does the insurer allow it?
Good point and it might be worth checking. I know some schools/clubs only allow you to fly PIC from the RHS after a specific checkout. Makes sense.