Does every single piece of animation need to be animated individually?

I want to create an animation like this one: http://www.arthurdepins.com/petites_animsflash/NetClubAnim-s.swf

Question: Does every single piece in this animation need to be animated
individually?

Answer: Yes. But not every at every frame. Some motion can require keyframes every 30 frames or as often as every 3 to 10 frames. Lip Sync may be done every frame to get it smooth.

Question: If so, do they each have their own separate layer?

Answer: Yes. Each animated object must be on its own layer, so that each object has its own unique set of key frames.... It is the Key frames that have the tweens.

Question: Wouldn't lots of layers make the file huge?

Answer: No. Most objects drawn in flash or imported from illustrator (simpler shapes not massively complex shapes) will make for a small file.

Question: What Makes a Flash File Big?

Answer: Importing big JPGs, Music Video and Complex Illustrator files.