As both questions asked, are buddypress issues, I found elsewhere the solutions…
Just to help out other fellow forumists, here are the solutions:
1. First, hide the toolbar for guests just browsing your website. This can be done in WP Dashboard > Settings > Buddypress > Settings tab > uncheck the first line
Then, in order to hide the toolbar from all registerd members, but keep it visible for admin, you have to install “WP Admin No Show” plugin and blacklist the role in which registered users are being assigned.
2. After you have hidden the toolbar, registered user can create a Group from ( mydomain.com/groups/ ) page!
Probably there is small bug to puddypress files which causes the “Create Group” button to hide in the profile’s group page menu ( mydomain.com/members/myname/groups/ ) although in buddypress settings, user can create groups is enabled!
Cheers