Thanks all, there are definitely some advices to consieder. I will first focus on the dust/dirt (checking allergy and clean fan regularly) - I´ve put a short summary on top so maybe other users looking for same feedback might get a quick overview.
@Darbycurrie: I am from Germany and air conditioning / edhumidifiers are quite uncommen here, so I can tick this off my list. But sure, heard from other people that air conditioning can cause some problems regarding ones health.