Yeah, I’d avoid editing the BuddyPress plugin file directly too, since an update could overwrite the change. I’d first check whether the theme is overriding the avatar template, and if not, Loco Translate sounds like a cleaner way to change that text.
The term is actually created/deleted, so it does seem more like something is going wrong with the admin response or JavaScript afterward rather than the database operation itself.
You’ve already ruled out the theme and plugins, checking the BuddyPress server-side logs would probably be the best next step to see why the group creation request is being rejected.
I agree, having everything under one BuddyPress menu would make the dashboard much cleaner and easier to navigate. It would also make it simpler for new users to find the settings and features they need.