Is it possible to shutdown a Windows XP PC via a set timer?

Well... kind of.

Getting a PC to shut down at a specific time is not all that hard. Getting it to start at a given time is more complicated, since if it's off it can't be running the program to tell it to start. However, some PCs do have a feature that allows them to go into a "sleep" mode and "wake" when they receive a specific signal.

There are also "nannyware" programs that can be used to restrict computer use to specific time periods, outside of which the computer cannot be used without supplying an override passWord (it's still ON, you just can't use it to DO anything). I've never personally used one, so I can't vouch for how well they work, but I know they exist.