"Performing Pending Operations..." instead of checking my mail

The message that you tried to send is probably stuck in Outbox, but it looks like Envelope Index may have gone awry as well, so let’s re-create both:

1. Quit Mail if it’s running.

2. In the Finder, go to ~/Library/Mail/. Make a backup copy of this folder, just in case something goes wrong, e.g. by dragging it to the Desktop while holding the Option (Alt) key down. This is where all your mail is locally stored.

3. Locate Envelope Index and move it to the Trash. If you see an Envelope Index-journal file there, delete it as well.

4. Move any “IMAP-”, “Mac-”, or “Exchange-” account folders to the Trash. Note that you can do this with IMAP-type accounts because they store mail on the server and Mail can easily re-create them. DON’T trash any “POP-” account folders, as that would cause all mail stored there to be lost.

5. In the Finder, go to ~/Library/Mail/Mailboxes/, locate Outbox.mbox and move it to the Desktop if you want to preserve any messages waiting there, or just trash it otherwise.

6. Open Mail. It will tell you that your mail needs to be “imported”. Click Continue and Mail will proceed to re-create Envelope Index — Mail says it’s “importing”, but it just re-creates the index if the mailboxes are already in Mail 2.x format.

7. As a side effect of having removed the IMAP account folders, those accounts may be in an “offline” state now. Do Mailbox > Go Online to bring them back online.

Note: For those not familiarized with the ~/ notation, it refers to the user’s home folder, i.e. ~/Library is the Library folder within the user’s home folder.

You’re welcome.

The contents of the IMAP account folder should match the contents on the server — no more, no less. Could you please clarify whether this is the case?

At any rate, don’t delete the Mail folder currently on the Desktop if it contains data that you want to preserve and that is currently nowhere else...