Thanks for your insights. You are right it might be that Crossfit-training here differs from training in the US.
Watching a few crossfit videos on youtube, I too noticed quite a lot of bad form. Generally AMRAP-type workouts seem to encourage bad form and personally I don't like them as much as having a fixed amount of reps/sets to do (I tend to lose good form "in a hurry").

They offer a free trial day at the new gym and I think I'll give it a shot and see if I like it.

Another question: Do Crossfit-gyms/trainers generally advocate a certain type of diet ("Paleo"-diet?)?