I can confirm I disabled BP Cover Photo plugin and now I can properly administrate the Group from the back-end.
This can’t be the final solution of course, but since Cover Photo is not mandatory at the development stage for my project it is a very good workaround for me!
colabsadmin is right, 2.3.1 exists and has been released three hours ago.
For the moment I just can confirm that, as you suggested, I tested Group Privacy settings by front-end and this is working fine.
Adding members to groups from wp-admin is not working at all. I believe all the changes in the wp-admin done to groups (for the moment I tested add members and change privacy settings) are not committed to the DB.
I will provide the error logs as soon as possible.