I'll be 33 and I own and still play my PSP. I worked with several guys who were in their 40s and 50s who played Gameboy Advance (they were obsessed with Pokemon Sapphire and Ruby). You may not see people above 13 with a GB or PSP, but I see people above 13 with GB and PSPs. You are aware that the PS Vita was aimed at teens and college students specifically?
I would not. I did used to love my Gameboy (had the original, and owned each iteration though the Advance SP), but that was for the type of games. Modern games don't tend to translate well to a portable platform.
I actually might, I'm thinking about the titles that I miss from that console: Conkers Bad Fur Day Live & Reloaded, Psychonaughts, Whacked!, Scrapland, Mercenaries Playground of Destruction, all of the MK titles for that system rocked...
The original Xbox was passively cooled IIRC so you should be able to get it into a neat little package these days. The power requirements weren't all that bad either, I remember it being something like a 120W Foxconn; I know for a fact it was a mini-ITX form factor but that doesn't apply to this context I guess. I guess whether I purchase it or not would hinge on the display and\or portability of the media.