Hi Andy,
I've just got home from a great birthday outing to... yes the US Embassy for yet another M-1 visa.
Anyway I'll try to help answer your questions!
If you apply to have an FAA PPL issued on the basis of your JAA PPL you will have an FAA PPL issued under FAR Part 61.75.
What this means is that your FAA PPL is a full FAA PPL but ONLY valid when your JAA PPL and Medical are valid. Your FAA PPL will also carry any restrictions that your JAA PPL does.
One such restriction on UK JAA PPL's is that flight out of sight of the surface (but not in IMC) isn't allowed. So as your FAA PPL will have the same restriction, you'd have to abide by staying in sight of the surface at all times (even if you have an IMC as the FAA don't recognise that rating). (FAA PPLs don't have the restriction). But then again the UK CAA have a pretty good rule there anyway! (IMHO).
Also if you don't have a night rating on your UK JAA PPL then you will not have a night rating on your FAA PPL. If you do have a night rating (or whatever it is called nowadays) then you'll have the automatic right to fly at night on your FAA PPL.
As you'll have a valid JAA Class 1 Medical (2 would surfice) the FAA will recognise this as long as your JAA PPL is also valid. You will *NOT* need an FAA Medical no matter what the school tells you - check FAR 61.75 for proof of this.
When you go to the FSDO to pick up your FAA PPL you will initially be given a temporary airmens certificate (FAA PPL). This is valid for 120 days whilst the Oklahoma office send out your permenant copy... (credit card style). This temporary certificate allows you to take flight as soon as you have it in your hands (assuming you have already had your FAA Bi-annual Flight Review / Checkout)!!! This is all free of charge from the FAA's point of view. ** UK CAA please take note of this!!! **
Hope this helps,
Charlie Zulu.