1) Yes
2) Yes
3) Yes & No... the phone probably only has the headers stored or has limitations on how back it downloads to the phone (default on the phones is usally 3 days)
4) ??? How is that moved? The pst should be same as exchange
Extra Credit - Yes on the phone go to the messages/menu/options/outlook email/highlight email and choose advanced.
Let me know if you need me to be more descriptive