Nah its none of that, wifi is fine and apple mail is synced up properly. My main concern is the fact that the emails it mentions in the coding section stuff; are ones i've never seen in my entire life. Im concerned someone (likely a spammer.) has gained access and is sending spam mail to other people. I don't know much about emails but i know they aren't supposed to do this. Furthermore, it wont allow me to send or recieve emails on the account.
I don't think it would be a spammer. However reading through this, It appears that the email bounced back because the client certificate wasn't requested by the server when you sent the email. This can mean a multiple of things, like the certificate not working or needs fixed or being bugged. I wouldn't imagine it would be a spammer looking at this though. It mainly appears as a certificate issue