I think I can help with point 2. Sometimes (usually PC users) have trouble receiving attachments from Mail. A couple of things to check that should help: Mail>Edit Menu>Attachments and make sure 'Always send Windows-friendly attachments' is ticked.
Also when you add an attachment to an email to send it normally gets place 'inline' so that you can actually see what the attachment is. Control+Click or right click on it and select 'View as icon'. This should help.
There is some software available from Lokiware called Attachment Tamer which gives Mail much better control over the way Mail handles attachments.
For point 1, it might just be a temporary glitch with the servers that will correct itself.
I have an Apple me.com account and sometimes (although less so recently) I have had connectivity problems. The solution that seems to work is to delete the email account in Mail and then re-create it. So long as it's an IMAP account you shouldn't lose any emails as they should re-appear when you re-create the account (I'd still make sure I had back-up though, but that's just me ).
How did you set up the account in Mail - did you let it auto-configure? You can over-ride this and set up the account manually by holding the option key just before you click the 'create' button at the first set-up screen. It'll change to 'continue' and you should be able to input your data and ensure it exactly matches the requirements of BT.