Hi Ant, yes overall would have done.
1. Envelope index and plists.
2. Then if not worked renamed mail folder. Removed plists. Nuke and pave mail accounts.
Restart and setup. There is plist caching in Mavericks which has caught me out a few times.

TBH I think he might have folder mapping woes and maybe Root folder path issues.
It's an different kind of IMAP gmail :-) and after needs tweaking on server and client side. we have had odd issues even with the We just say use chrome browser and webmail until We can sort it out.

Another trick we use is just to use the download headers first for first sync then toggle all mail and attachments setting.

You should only see this for IMAP and Exchange accounts.

In Accounts, under the Mailbox behaviors tab select to NOT save to server. Save to the local Drafts folder. This will stop the extra copies in drafts.

Mail saves a messages as you are composing and creates a draft message. It should remove when sending but often does not creating confusion.

Yep long standing bug. But 99% of users I work with want drafts in sync between devices and although using local Drafts is a fix it is not ideal for multi device people.