1) Yes, atleast the certificate which contains the TLD even if you use SSL, the full contents if you don't.
2) If you are not using TLS or SSL to access your e-mail server, he doesn't need to "crack" anything, he can just read the password being sent on the wire and can see all your e-mail. Use of TLS or SSL when connecting to your mail server will prevent this.
3) If he was any good, you wouldn't be able to, but keeping it patched and running a firewall should provide reasonable protection.
4) See each individual answer for countermeasures. Additionally, you could use an encrypted VPN. He'd know you were using the VPN, but the VPN would prevent him from knowing anything you were doing. This, however, requires a VPN provider and the VPN provider would still be able to tell the same info you are worried about the owner doing.