Hello Elaine,
Thank you for reaching out to SmarterTools. I am going to tackle this one point at a time.
Remove emails every 24 hours.
For this you can set up a Folder Auto Clean rule that will delete messages that are older than a day.
Restoring emails
If you have "Archived Messages" enabled you can restore any incoming message to the user mailbox or other folders. To speed this up or automate it you can leverage the API.
For the sent items. This can be grabbed from the archive message as well if you are capturing both directions and can do the same.
Once this is done the user can then sync them down to the outlook account.
I hope this helps.
Thank you
Tony Scholz
System/Network Administrator
SmarterTools Inc.
www.smartertools.com