problems with user registration

Disable non-core CB plugins 1 by 1 and see if the issue goes away. If you have Joomla caching enabled then disable it and purge cache.

I took it off and put cb with less plugins, now there are only the essential ones!
and now also the registration page and inaccessible and asks me!

You had "Allow User Registration" set to "No" within Users > User Manager > Options and you had "Allow User Registration" in CB > Configuration > Registration set to "same as global `allow registration` site setting". This basically means you shut off registration. I've reconfigured this for you and your registration is enabled again. Please read your documentation available for download in the Advanced downloads section carefully as this is basic CB configuration.

Suggested reading and viewing:

www.joomlapolis.com/documentation/community-builder/getting-started
www.youtube.com/playlist?list=PLp0puRITgC7PuyzPsMUECDI46VE7IFSAX

maybe that happened yesterday while I removed and then installed cb with the hope of solving the problem ...
however, now I get the following message:
Your session has expired and / or cookies not enabled on your browser. Please, refresh / reload the page before you write about it.

never had so many problems with a component I are offering to make it even more intuitive?!?

Your session issue is due to the 3rd party system plugin "System - EU e-Privacy Directive". It's preventing CBs cookie and session from functioning properly, which results in CBs spoof checking to always fail. You can try shutting off spoof checking within CB > Configuration > Integrations, but it's not recommend and it may not resolve your issue.