As you can see the top level URLs are broken
I see that in the markup you've pasted here, but I can't reproduce it on my current setup. What URL are you looking at when the nav menu is rendered? Is it a user page (example.com/members/foo/)?
groups-personal-li id is used twice
Confirmed. This does look like a bug. It looks like bp_nav_menu() has code that's supposed to prevent these sorts of duplicates, but I guess it's not working.
I really can't appreciate the difference between Memberships or Groups Top levels
I don't believe that Memberships is supposed to be a top level item - I think it's supposed to fall under Groups. I'm guessing that the nesting is breaking because of whatever's causing your top-level URLs to break.
the Messages Top level menu disappear, and except the submenus of the TopLevel? Activity the others doesn't have all their sub-menus.
Ditto. I'm guessing that something funny is happening because of where you are loading the menu, and this is the single cause of several of these issues. If you can provide more info about how you're using bp_nav_menu(), it'd be helpful.
found a 'solution' about missing submenu items, but I'm not sure if it's gonna be soo good.
You're right, it's not good :) It will allow anyone to edit anyone else's settings.