Download size/time of iTunes Movies and Rentals + Apple TV use

A single movie will usually be between 1-2G. The amount it will want to buffer will depend on the speed of the buffering.

Having a reliable sustained download speed of about 300K/s then it should buffer and start playing within a few seconds.

The Apple TV has 8 GB internal memory for buffering (You can't access this and you can't put your own files in that memory). Rentals (just like Netflix) only need to buffer a very small part, so they play almost immediately and stream after that.

I don't know how much of the movie it keeps, but even if you fast-forward it always only downloads a minimal part of the movie.

I don't think you can purchase movies on Apple TV, only rent them, but I may be wrong. I don't know how purchases work, but for rented movies it simply downloads whatever it needs to start playing back from Apple if it's not in the buffer.