Mini for son.

my son has been playing flight simulator x and call of duty on my computer via bootcamp. I want to get him a mac on ebay.

Would a mac mini 1.6 duo run these games better than a pentium 4 3.0 with a nvidia 5200?

Also I know the mini uses the system ram for graphics, if I put more RAM in it will the gpu use more or will it stay at 64 MB? Can you change the amount of RAM it uses?

Id forget the macmini right now unless space is of a premium and you just want a mac for working.
On a good day you can pickup a 17" intel core duo on ebay for £500. So, sell the monitor you were going to use for the £399 mini and you get enough to buy it so your son can play COD etc much more effectively and be assured that he is getting a much better mac for the money.
Feel free to post any links you find and i can help you judge wether the auction is trustworthy or not.

Can you upgrade the graphics on the imac?

the high end 1.83 mini and the low end imac share the same graphics.

AFAIK, only the 20" & the 24" have upgradeable Graphics. But Apple's quoted prices are for production line orders only.

Yeah, dont bother with the educational model. Get the 1.83ghz dual core 17" imac with radeon x1600. For the price it is a much better buy than even a top end 1.83ghz mac mini even with maxed out ram.
If nowhere else, try the refurb store on the apple website