1) There's a setting in the Invite module for "Enable Automatic Resizing". This should take care of your problem, but there are some cases when it won't. Please note that we have no control of what's in that pop-up, and it always opens to the right, so if you have it in the right sidebar, it may go off-screen.
2) In the Invitation configuration, there's an option for Full vs Condensed view. To show the user's avatars, you want the full view.
Hope this helps, but if not, let us know!