WPA Enterprise means that Users would login to the wifi network with their own credentials instead of sharing the same password (PSK). This tends to require some sort of back end authentication server. Think of it like a windows network setup. At home, people will likely have one account on the computer that is shared. At work, users each use their own username and password to log in, and they authenticate against the domain.

As for the problem you are seeing with the 3GS, I haven't seen similar, but I normally go between WPA2 at home (on an Apple Airport) and open public Wifi.

As for the Airport, yes, they can operate as just a base station.