1. Sure.
2. Yes, DCs cannot be moved between domains (they *are* the domain).
3. Given that you're moving to Domain B, no.
4.
Always :)
If you want permissions to work across the trust during the migration check out SID Filtering (on the Trust).
Groups, Users and Computers can all be migrated and it generally works best in that order. Groups and Users can be migrated more than once (synchronising group membership, etc).
Depending on size, some computers will fail to migrate. Make sure you know what to do if they fail.
Passwords on user accounts will migrate if you configure the necessary components.
Anything more complex than file servers and DCs running in Domain A?
Chris