Mail opening multiple untitled windows...

Quit from Mail. If necessary, force quit (you will lose unsaved changes if you do so), by holding command-option-escape keys down and selecting Mail from the Force Quit menu and clicking force quit.

When you reopen Mail, try with the Option key held down. if other windows open than the inbox, command-option-W will close all windows while keeping Mail running.

I have this problem, too, and followed @a brody's suggestion. Mail started with the Option key held down and a 'zombie' window appeared. With command-option-W the message window closed, but the 'zombie' window is still open. It's only one 'zombie' window now. It was 10 'zombies' in the past, so the approach seems to have been rather successful.... ;)

Still, I'd like to get rid of the last 'zombie'

That's a good item to check. Thanks. I don't have any drafts in any mailboxes that could lead to the creation of the 'zombie' windows. It would be something else...