Can you copy the session to a different folder or repository

1) we can, but we have to copy the mapping first and then we
have to copy the session....

2) Folder :Yes
Repository: No.

if you want to move the session to another repo, then you have to export the session and then import it in the target 
Repo.
This assuming that the mapping has already been moved.

  3) In addition you can copy the workflow from the Repository manager.
            This will automatically copy the mapping associated source targets
            and session to the target folder. 

4) Yes. By using copy session wizard u can copy a session in a
            different folder or repository.But that
            target folder or repository should consists of mapping of that
            session.
            If target folder or repository is not having the maping of copying
            session ,
            u should have to copy that maping first before u copy the session