1) A Carnetix DC-DC unit like the 2140 or the 1900 would probably be the best bet for powering the PC then.
2) If he wants it for music, how is he going to see the PC if his only screen is a 19" screen? Or will he only use it from the rear of the vehicle? I've seen some large screens in a dash, but 19" would take the cake. Light gaming like SNES or N64 emulation is likely doable. DVD playback will be no issue. Is there a plan for Internet access yet? I have a rooted Android phone with Wifi tether for mine, that's the simplest solution that I've tried so far.
3) An inverter is probably fine for the monitor. I would definitely stay away from it on the PC though because you will experience issues in the audio such as ground loops. No, a ground loop isolator is not a good solution to this, good wiring is.
4) Sounds good on the input front. Pricey, but good.
5) Aux input is also the preferred way so that's good.
6) I figured touchscreen was out. No GPS is one less expense.
I was a little frightened by the $250 PC budget. DC-DC PSU + Inverter + DiNovo + MCE remote is probably over budget already and there isn't even a PC included in that price. I'd recommend doing a lot of reading over at mp3car.com for more info. I haven't really posted over there in a while, but they were very helpful in the past and there is tons of useful information there.