1. Yes, the Disk System works on the AV Famicom.
2. The AV Famicom has AV Composite output; something the original Famicom lacks entirely. You'll either need to have an original Famicom modded for AV / RGB / Whatever or use the RF it outputs. This is problematic even if you do have a TV that accepts it; Japanese TVs had different channels. 3 or 4 on the Famicom's channel selector is something like 95 on a USA TV. Also, RF looks like garbage.
3. If you hunt around you should be able to find a complete AV Famicom for around $100-$150. They're fairly common in Japan since they were made for so long, and boxed ones aren't that tricky to get.
Other stuff:
The AV Famicom originally came with two controllers that have very short cords. They also did not actually come with AV cables; the SNES or N64 ones work fine though. See if you can get one with the plastic cover on the side.
The AV Famicom can use NES controllers, but the light gun is some kind of different story. I think it natively uses the Japanese version that plugs into the side, but cannot take the USA Zapper without a mod.
Check out the Twin Famicom or Twin Famicom Turbo if you want another option that involves the Disk System. Might save you some money, though the audio on the Twin is muffled (both version) without a simple mod. No mater what Disk System you get though, make sure the belt has been replaced recently. They rot and fall apart.