I read many bugs often under Windows10. Is the galaxy2 working better with older windows ?

I'm not sure to understand what the difference between "Galaxy specific" and "Client itself". For me client = Galaxy and Galaxy=client.
what do you mean ?

Sorry, if I was unclear on that. What I meant:

Most error seem to relate to "internal" problems, e.g. problems with the games database, connections with services, memory leaks, etc. but rarely its a problem that relates to the Galaxy client interacting with its environment like, crashes on startup, access rights problems, random deleting files, causing sideeffects (like installing a library that other applications are dependent of which arent't starting anymore), etc.

Is this more clear ?

Well, what I understand is that you confirm that the Galaxy is buggy even under Windows7 and as it is not officially supported, it is certainly worse on W7 than on W10.
As a result, I understand that galaxy 2 should not be used on W7 systems.
Am I right ?

No, I can only confirm what I already wrote - as most people usually aren't saying what WIndows version they use.
You can use Galaxy 2 on Windows 7 just don't expect gog to give you support in that case.
Peronsally, if I would still be using Windows 7 I would try Galaxy 2 as - as said before - most problems seem to origin in Galaxy 2 itself not in its interaction with its environment (it is still a Beta version, so errors are to be epected regardless of the underlying operating system).