1. IF your work email is a BES account, yes.
a. Ask your BES Admin to push the BES mail folder to you:
ReadKB12610 Email messages associated with a BlackBerry Enterprise Server and a BlackBerry Internet Service account are located in the same Messages folder
b. Get the third party app for doing so Empower Work Folder for Blackberry BES
2. No, you can't synchronize AOL mail, sorry.
3. Yea, on the BlackBerry, in that Message folder, scroll to the most recent date bar separator and choose Menu > Delete Prior. All gone.