SSL Certs don't require a reverse DNS match,long as your domain responds to the domain name used,and the cert matches and the cert provider is listed...
Whoever registered domain loaded custom DNS. Should you wish to tinker with the DNS you'd need to log into serve hosting's panel or transfer the DNS...
Well if they block outgoing ports you're pretty stuffed unless the app can route over open ports. Maybe elaborate on your download methods and if you...