Yes, the holder of a JAA ATPL is eligible to be issued a FAA ATP certificate. The actual hour breakdown can be found in FAR Part 61.159 but at 10,000 hours you should have all the squares filled.
You can study for the "knowledge test" by book or online, there are even apps to study on your iphone.
The FAA web site lists testing centers. It looks like the only sites in Europe are at Farnborough and Le Bourget.
There is an oral exam as part of the "practical test" (checkride.) Normally for a type ride it covers airplane systems but anything is fair game. If you do good on the knowledge test most examiners just focus on the airplane but if you have a low score on the written an examiner can poke and probe. Old FAA guidance said an oral should take about 2 hours, I've heard of them going anywhere from 45 minutes to 4 hours.
You need to do the sim ride in a sim that has been approved by the FAA with a FAA Inspector/Examiner watching. The FAA web site lists all their approved sims. Any sim center should be able to tell you if they can do FAA checkrides.
Again, the FAA web site allows you to search for an AME. You will need a First Class medical certificate, not all examiners can perform a First Class exam.