1. Not exactly sure about the exact file size, but I downloaded DK for NES, and it downloaded in under 30 seconds. So, I'd say no more than 2MB (although, later systems may be bigger, it was only an NES game)
2. Yes, you can get USB adapters for your computer or for the Wii (either wireless connected to your computer/same one for the DS, or wired to the Wii. and yes, the wireless one does work through walls.
3. No clue, but I'm gonna guess no Reggie