I use IMAP, I can't imagine going back to using POP3.

Yes, the mail app will download and cache messages that have been read using IMAP.

I don't see how the app could possibly sync sent mail back to your other client when using POP3. POP3 is fundamentally a readonly/delete protocol.

On IMAP delete, are you sure that the Trash folder that it is using exists. You can configure on the phone which folder it will use for Trash.

The iPhone IMAP client is the best mobile IMAP client I've used, for me at least it just works (something I could never say of the WinMo builtin one or the various third party clients I tried on WinMo).