BuddyPress.org

I simply don’t get what you are trying to do here and you seem to be over complicating things.

Simply click the link to ‘groups’ in the main set of menu links this is the groups directory view and on that page should be seen a clickable link ‘create a group’

This isn’t anything to do with adminbar, nor do you access this via a url which actually would be http://example.com/groups/create/

Your bp default theme either shows this or it’s a defective incomplete install your other questions are related to third party plugins and / or themes and at this stage we are simply trying to establish that bp-default works before moving on.