Damn, sorry.
Ok.
1. Yes. Apache AND nginx use the same certificate.
2. Ubuntu 14.04.3 LTS and Plesk 12.5.30 Update #62, nginx version: nginx/1.11.1, openssl 1.0.1f
3. Yes. No firewall blocks port 443. And yes, Fail2Ban doesn't block this port.
4. No, I don't have SELinux installed.
lsof -i...