A standard AirPort Base Station will serve up DHCP addresses, so I would assume that the new version will to. You can do many gateway router functions with the original type, particularly if your entire network is wireless.
You shouldn't have any problem setting up any of the computers for a wireless connection through 802.11b cards, but I don't know if anyone's come up with hardware for anything other than Macs to take advantage of the Extreme's capabilities. You do not want to make your printer DHCP. You need to assign it a fixed address (outside the range your DHCP server uses) so that your computers can find it.