hi there, fullsail student at your service. i have been attending fullsail university's game art program for 8 months now and ill try to answer your questions.
1. game art and computer animation are said to be close to the same program but it is the fine details that make the difference in them. for example, in game art you will learn about UDK(unreal development kit) witch is used by a ton of game developers and will really help when it comes down to careers.
2. if you want to do animation in games and movies then go with computer animation. the animation from movies to games isn't that different and i am sure that you will learn more animation from the computer animation side.
3. i hate to say that you don't need much free hand skills to make it but it is true. i suck at solid drawing and animation if it is free hand but i still made it through the classes. now this doesn't mean that you don't use drawings at all. trust me when i say that it is easier to learn from 2d to 3d.
good luck, you'll need it.