I'm not sure whether you can do that. But you can give it a try.
If you want to access email, I believe you should SSH to E-mail server. You can find out the E-mail server name via DH panel --> Mail --> Webmail
It should be your full email address. Or your email name (something like mxxxxxxx). You can find them out via DH panel --> Mail --> Manage Email
smtp: mail.yourdomain.com port: 25 or 587
pop: mail.yourdomain.com port 110
Yes. You can always save your current session and it will be listed in saved sessions.
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