a- If it watch the whole movie, yes, it does download the whole 20mb, if not it depends on how many megabytes the player has buffered before the viewer goes to another page.
b- It depends on the resolution of the movie and the codec used, usually if the movie is PAL or NTSC, then 1500 to 2000 Kb/s it's ok, less than that will degrade. If is 720p you have to go higher because it need more kb/s to keep the quality.
Also, no many sites use flv anymore, the most common use right now ( when it's a flash player ) is to create a flash movie container with the player and stream a mp4 video file, has better quality and it's more portable.
Here's a clear explanation and examples to the streaming and the resolutions: Exploring Flash Player support for high-definition H.264 video and AAC audio