Gmail IMAP *was* working with Apple Mail - days later it's stopped working.

Question

Hi all,
I recently started my Gmail IMAP account over in Apple Mail and Mobile Mail in order to get it working properly across an iMac, iPhone and MBP. I followed Gmail's IMAP settings to the letter and the only thing I couldn't get working was for the Trash folder in Gmail's server to take the place of the Trash icon that Mail has. While Sent and Drafts were represented correctly once I did the "Use this Mailbox for..." thing, Trash never moved up there.
Turns out that when I've been deleting emails in Apple Mail, they haven't been deleting in the Gmail inbox. They just sit there, label free. In the meantime, the fact that the server Inbox is stuffed full of label-less emails isn't reflected in the other applications, and deleting an email in Apple Mail does not delete it from Mobile Mail. Similarly, mails I've moved in Apple Mail from the Inbox to the Gmail folders are not reflected in Mobile Mail, where they remain in the Inbox. Furthermore, on the server the mails appear to have the correct label for the folder I moved them to in Apple Mail, but on the server they are still in the Inbox.
I'm confused. The Gmail server inbox seems to be acting like All Mail now - in that I move something from the Inbox and into a Gmail folder using Apple Mail or Mobile Mail, but on the server they just stay in the Inbox and have a label added. They sit in several places at once. This is not what's supposed to happen!
Furthermore, now any emails I write in Apple Mail and Mobile Mail start saving drafts every few seconds then saving these as new emails in 'Drafts', and on the server saving them as multiple different versions of emails. If I send an email, I do not need to save every single variation every 10 seconds. Even if I don't send an email I don't need that. It wasn't doing this before, why has it started now?
I thought I'd got this all sorted but clearly I don't.
How do I achieve the following:
1) In Apple Mail and Mobile Mail, have an Inbox, Drafts, Sent and Trash box at the top, in which changes are reflected on the server and vice versa.
2) If I move an email in the above software from Inbox to a Gmail folder, the email on the server moves from Inbox to that folder, but remains in All Mail.
3) If I delete an email on the above software, it's moved from wherever it is to the Gmail Trash folder, where it's deleted after 30 days. It does NOT simply lose a label and remain in the Inbox or even in All Mail. If I delete something, I want it gone EVERYWHERE.
4) Don't save my Drafts every 10 seconds. Ever.
It can't be that hard to do this, can it?

Answer 1

Hmm, turns out my iMac Apple Mail has been resetting the Mailbox activity settings for some random reason which would explain the drafts problem. Wonder why?