Yeah, the IP address is basically the current address of your computer on the internet. Each connection has to have a unique address, although it's possible to make multiple computers on one network appear to be behind the same IP using ICS or NAT and/or a router etc. The IP for the connection still remains unique though.

Depending on the ISP, your IP may or may not change each time you reconnect - mine doesn't change

As for the firewall, ZoneAlarm might be better for most people, Tiny can be complicated if you don't know what you're doing, and one slip-up will knock you off the net completely, it's that powerful