HR,
taking FAA writtens is easy. You can learn every question/answer from the Test Prep series. Only the instructor rating FOI database has been changed considerably and thus (maybe not now, but fairly recently) it was harder to pass the FOI test. it's theory of instructing, but lots of ambiguous discutable answer options off one book.
You could get FAA licences in Europe, but it's probably not worth the hassle and cost, as sorting visa and dropping in to US, take the written at the school or school nearby, booked ahead, you show up, gone in one hour or less, with the A4 pass confirmation you present to examiner after checking logbooks, totalling times in form 8710 and whatever flying 3hrs+ needed.