Hi- you’ve got some great tips here so let me add on. We live in Hong Kong but my husband is German and my daughter attended a German gym camp this summer.
1. First, it depends on what your goals are for your daughter. If she’s rec level, then you may be able to find this at her school if it is a private school (my friend’s daughters take this route)
2. Germany’s gymnastics program is standardised at a federal level and implemented locally. There aren’t really private clubs. German standards are set according to age category by the DTB (Deutscher Turnerbund). You cannot compete in a level outside of your age bracket. it is an up or out system to be in the most competitive streams. The guidelines by age (or Altersklasse) can be found here:
https://www.dtb.de/geraetturnen/downloads/leistungssport-weiblich . There are two sets of requirements: technical and athletic. The technical requirements are what you do in regular comps on each apparatus. Athletic norms test conditioning, strength and flexibility. These are tested in December prior to meet season
2. Each state has a system of clubs or “Verein” which are federally endorsed. Each state will also have a certain number of talent schools “Turntalentschule or TTS”. Your state is Hessen and the poster above has given you some links. You’ll need to join a Verein but this is pretty straightforward.
3. For the competitive stream, they will not take kids older than 8 years old if they don’t have prior experience and you will be pushed into rec.
4. All of the information is in German, but many coaches - especially younger ones - will speak at least some English. My daughter has proficient German but said one of her coaches over the summer spoke fluent English.
Hope this helps!