Hi,
I think I can answer your 3 questions.
First off, I assume you have the legal right to live and work in the EU, if not then it is pointless to do the JAA licensing.
1. The JAA is the governing body of aviation in the EU; HOWEVER each individual country can intrepet the regulations as they see fit. You have to get the "ok" from the EU country from which you wish to receive your license. Each JAA nations is different. Some countries will insist you take a ATPL theory course, other nations may waive this. You need to do the research.
2. You can do the JAA Comm/ME checkride in the USA. HOWEVER; it is illegal for the USA to issue the IR. This is impossible. You can doa JAA Type Rating in the USA on a jet, the company in the USA can issue the Type Rating, but you will still not have the ATPL because that will need to be issued by the respective country in the EU. Even if you coordinate with the EU nation that you will do the training in America for a Type Rating in order to get the ATPL, you will still have to do a couple things in the actual aircraft. So if you get a 737 Type in the USA and have a JAA examiner at Simuflite in Dallas observe your checkride....it still is only half the battle. you will need to charter out an empty 737 and do a checkride in the EU, then you will receive your ATPL. The other option is doing the Type in Europe at a JAA certified TRTO, then you ca do everything in the sim. Simple economics my friend. The TRTO's lobbied the JAA and convinced them to make a provision that helps keep the training in Europe, so they can charge 5 times the price.
3. Your ultimate goal is the JAA ATPL. This again has to be issued by the JAA member country, i.e. LBA in Germany, CAA in the UK, etc. There is no such thing as THE JAA LICENSE, the license will be issued by the respective EU nation and have the words JAA somewhere on the license. The best example is if each individual state in America issued its own license and conformed to the regulations set out by the Faa. Obviously in America you receive the FAA license and it says nothing about which state it originated from; however in Europe each individual country is responsible for licensing.