Click back and click on Access cPanel again. It doesn't always work on the first try.
Or try yoursubdomain/cpanel which will redirect you to the cPanel login.
I prefer IMAP.
For your login, you should use emailaccount+emaildomain.com. cPanel requires the plus sign instead of @ when logging into the e-mail account.
IMAP will sync changes to the server, whereas POP just downloads the mail from the server to your client. You can use Secure Password Authentication for outgoing.
Did your account become inactive? If so, then it is long gone. I'm not sure what you mean by add you to the cPanel database, because that's not how it works.
Clear your browser cache, change your DNS servers to Google public DNS, or you could have even been blocked by the server firewall. There are a lot of reasons.