Scorep.,
I did my EASA ATPL(A) to FAA ATP MEL just recently.
I understand you've done your verification. Good.
For the FAA ATP knowledge test (aka "written test") you will have to pass this prior to your FAA ATP check ride (flight/sim skill's test), normally people doing conversions combine this with their TR skill's test. The examiner will need to see the confirmation of passing the knowledge test letter on the day of your FAA ATP flying test. This should be the original.
The FAA ATP flight test is basically just part of the Type Rating check-ride - although I believe it's the full check-ride as opposed to what the American's do for their recurrent's (which is a more like progressional training/checking). Mandatory part of the FAA ATP check ride will be what The Americans call the "oral" - which we don't do under EASA where is's written. The "oral" is usually type specific, if combined with an Type Rating check ride, and will be focused on limitations and system knowledge of the aircraft type in question.
The FAA ATP check ride is quite relaxed and straight forward, with the Americans focus being on general handling skills.
After the check ride you should be issued with a Tempo FAA ATP MEL and whatever Type you did your ride on.
Don't forget that you will need to have your FAA medical passed before the check ride. I think the check airman (EASA for TRE) will require to see this. I recommend filling out the FAA medical form via their online system - to which you should be able to gain access already now.
You should also try and gain access to the brilliant FAA IACRA online licence system. I had the help of an FSI instructor to do this, while I was present, so don't know how easy this is without. Don't forget the FAA is know to be a bit anal about correct addresses, names etc. - simple errors of medical address not corresponding with IACRA details etc. can seriously cock up the licence process.
With regards to the CBT for the knowledge test. I used dauntless - which I found to be ****. I did my test in the US at an ATP (actual name) school facility, which included the "training", and did the exam straight after. Very easy.
Finally - good luck with it.