Q: Questions about the Airport Express 802.11g

1. It should, though your older Express is not capable of many advantageous features of newer AirPort Base Stations.
2. You need a version of AirPort Utility earlier than 6.0, depending on the version of OS X you are using.

Lion, Mountain Lion: AirPort Utility 5.6

Snow Leopard: AirPort Utility 5.6.1

Leopard or Snow Leopard: AirPort Utility 5.5.3

Tiger: AirPort Utility 5.4.2

Panther: AirPort 4.2

Jaguar: AirPort 3.1.1

even older versions: http://support.apple.com/kb/HT1998

Its pretty good as an ad-hoc wifi network to share files around and its easy to take with anywhere you go.   The option to plug directly into the wall power socket makes it really nice.  Apart from that its really out-lived its design purpose.

Not really, you can still use it as an AirPlay or print server. I hadn't thought of using it for ad-hoc.

The option to plug directly into the wall power socket makes it really nice. 

It is a clever design feature, but wall sockets are often behind furniture and usually near the floor - both less than ideal locations for a wireless device. Perhaps those considerations contributed to its elimination in the new model.

I hope the OP paid only a few dollars for it; much more than that is not worth it. The 802.11n Express is only about $50 used and much more capable than the original model, but at that price the new dual band Express should be seriously considered.