I have a problem with my ISP. They say that they don't block any ports and I have public IP, while I think these both statements are false. Before I talk to them again (which is really tough when my understanding of these terms is different than theirs) I would like to make some things clear.

It seems like my computer is behind NAT (is it possible to have public IP and be behind NAT at the same moment?). When I check my IP, through some external server, and type that IP into browser I get a home page of some router (not mine). Isn't that a proof that my IP isn't public?

Also, I have problems with making connections via some ports. E.g. when I'm trying to connect through some high port (> 1023) via SSH, it doesn't work. Is it possible that certain range of outgoing ports from my computer are blocked? Or is it simply because that my ssh client (PuTTY) can't receive incoming packets because of blocked incoming ports?

To avoid some questions: it's not a problem with my router, I tried connecting my PC directly and it also didn't work, while having connected by 3G using phone with USB tethering, it does work. Thanks!