Thanks Walter. That solves one half of the problem (keeping emails in Hotmail). What I am stuck with now is how, if I download and read/delete an email in Mail, how do I get Hotmail to recognise this? I can manage that from my iPhone (which I presume is an imap setting), but think the problem is that on Mail, its a POP account. Any ideas? Thanks
You need to check two things:
1. Log in to your hotmail account and check settings on it. Check if hotmail allow mail clients to remove/delete messages from server.
2. Open mail preferences->go to "Accounts"->Select your hotmail account->Check "mailbox behaviors" and check settings for "Trash". Make sure - if this option is presented - that "Store deleted messages on the server" is not selected.
Make sure to delete messeges from mail trash too.
I do not think Hotmail support IMAP. Therefore even on your iPhone it will have not an imap account.
I am not sure if you can sync Hotmail with iCloud.