Thanks for the detailed answer.
Given that I already meet the hour requirements for Multi Engine, Instrument Rating etc stated in Part 61 I won't have to complete any practical trainings, only theoretical ones and pass the forementioned written exams and checkrides? Also, is it in any way better to pass the IR and so on after obtaining the commercial or it costs and works just the same as if I only had the private certificate?
Lastly, does getting the TR on my private certificate make any real sense? As far as I understand I won't be able to use it for work in the US anyway, and the TR will most likely expire on my EASA licence before I get the FAA commercial.