The requirement for a medical is just wrong. The regulations (FCL.040 and FCL.050 and MED.A.030) require you to have a medical if you are exercising the privileges of a licence, or if you are a student flying solo. You do not need one to be trained.
As far as the training for the "conversion" is concerned, as a holder of the equivalent FAA licence/rating, as long as you have 100 hours [assuming you want to convert FAA PPL ASEL to EASA PPL(A) SEP] you have to take two theory exams and the practical test, the training is only as required to pass the test. You will also need (separately) a radio telephony licence.
However, you have to "hold" the non-EASA [ICAO compliant] licence and the rating, an expired licence and rating will not do. What the German LBA has to say about a non-expiring FAA licence that is not current I do not know, it is probably safe to have the BFR to avoid any doubt.
I do not know if EASA law is currently implemented in Germany, though, so you might have to wait.
And while German law indeed regulates where the PIC has to sit, the same law says that this does not apply to training flights. If they don't believe it, ask them to read Para. 4 (2), (3) and (4) of the LuftVO.
But my general advice would be, pick a school that has a clue and actually wants your business.