Medical can be done in Europe, you will find a list of AMEs on the FAA website-you need to register to MedXpress first.
There is no training required as long as you fulfill all requirements, but the written exam and the check will need to be done in the US (the check flight could be done anywhere, but you will need to do the written in the US).
You will probably need a TSA clearance as well, which can take up to 90 days.