1. Once you have studied the JAA PPL book, you'll need a quick look at the FAA question bank and you'll be grand.
2. The FAA PPL does not expire. To keep your FAA PPL current, you'll need a BFR (Biennual Flight Review) with an FAA Flight Instructor (CFI), which can be done in the UK and many places in Europe. Not really a test, just to demonstrate currency.
3. Do the first FAA medical in the US when you start training because it is cheaper, but renewing every 3 years (for a class 3 for PPL), can be done in plenty places in the UK and all over Europe.
4. You MUST have an FAA (FCC) RT licence, which you'll get in the post after applying and paying online, to be able to fly outside US airspace. This is not very well known by some schools and CFIs in the US because they don't fly abroad.
5. I believe there are some limitations on flying abroad (in other than UK airspace) on a G-reg with your FAA licence, not sure if that concerns you.
6. You're welcome. IP