Is there any way to edit the group, or assign a contact to a group while making a new one? I hate having to go into address book and then changing it, and syncing it again.
I think doing it in the address book on your computer then syncing is the only way... although that would be a nice simple feature to add for an update.
I do not think it is possible. If you use sync only for group feature, I would advise you to install an app to manage contacts groups on iPhone. There are many.