I'm using Csmenu so I don't know if this registry hack will work with Windows 7.
Open regedit and navigate to HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion
Create a key key named policies if there isn't one present. Now create the Explorer key directly under the Policies key.
Now right-click in the right hand pane and choose new > DWORD (32-bit value), name it NoFavoritesMenu and give it a value of 1. Restart you computer to see if it takes affeect.
I don't use the Homegroup, so I can't help you with that one.