Strange Mail behaviour - need help!!

Hi folks - can anyone help me sort out problems with Mail? I'm using BT Broadband with a BT e-mail address. Mail appears to download correctly, although the progress bar tells me I'm receiving 1 of 20, 2 of 20 etc... and often then only one message appears in any inbox. I usually get any e-mails sent to me, but often wonder what these others are and where they go... but this isn't the main problem.
Sending Mail appears quite slow, even a simple two-line message with no attachments can take ages to leave my Mac, yet other applications have a good Internet speed.
Sent items often go to Drafts rather than Sent, even though they've gone and are received perfectly by the intended recipient.
When I try to delete items, particularly bulk mail, they reappear as if never deleted, and I have to delete them again; sometimes this causes Mail to hang and I only discover this when shutting down and I get the message: "the application Mail prevented shutdown..."
Can anyone help resolve these? I've used Mail for years with no problems, until very recently.

Do you know if your email is set up as a POP or IMAP account

It's an IMAP account through Yahoo. I've just reopened it to find all seven deleted messages from my last trash empty all reappeared again.

Still doing this... without any out-going messages or any other apparent reason, Mail still prevents shut down until forced to quit - sometimes I leave it for up to half an hour, then try again, but it still appears in the top menu but with the quit option greyed out. any thoughts on why, or are there any known issues that may cause this?