3. I doubt you will be able to find a battery with enough power and small enough size to run it for a significant amount of time.
It's supposed to have a power draw of around 1W, isn't it? I mean, it says you need a 5v, 700mA supply to run the network one. I see this being a complete non-issue.
4. There's not much space to work with.
It's business card sized... a gameboy motherboard is significantly more than business card sized. Where's the issue?
You could just cut out the 2 AA port, cut the hole a bit bigger, and epoxy in a 4 AA port.
Throw in the screen, and you shouldn't be looking at more than 1.5A draw.
1 and 2 can be issues, but if he IS willing to run it all under a full distribution of linux, he shouldn't have too many problems.
Geb's a wild and crazy dude. I can tell, only the most adventurous people keep the hotsauce next to the deodorant.