You are asking excellent questions. Its an eye opening experience to see yourself snowboard. I will give my personal take.
I am going to answer your questions out of order.
4) The best angle is all of the above. It is beneficial to see your self from the front /side / behind. Different perspectives can give you a lot of different insight into your riding. It is very hard to accurately critique from a "POV" with like a helmet cam or holding a gopro on a stick.
2) I think the best way to get good video for movement analysis / critiquing is to have someone recording you riding down a slope from a static position (Your friend rides down stops and records you riding down and past the camera). Think about it. If someone is standing still recording you they will capture all of the angles you want. As you are riding down the slope they will capture a front on perspective, as you ride past the camera they will capture the side perspective, and as you keep riding past they will record you from behind. Holding the camera on a stick makes a cool looking video. Personally I dont think its that useful for analysis.
1) I bought a gopro last year on proform. its a sweet camera especially for the stick type video or POV. I found that it is lacking when it comes to getting good video from a stationary perspective (having a friend go ahead stop and video tape you riding down the mountain). Since the gopro doesnt have an active zoom (and the best lens mode is wide angle) you get only a very short segment of video that's useful for analysis. Unless you are really close to the camera you will appear very small in the frame making it hard to really use the clip for analysis. I am personally going to buy a true HD camcorder this season that has image stabilization and a nice optical zoom and 60fps recording (they can be very affordable). I think this is the best way to go if you are looking to get good quality video for movement analysis purposes. If I didn't get the gopro for half off I wouldn't have bought it. I don't think they are worth the 300 dollar price tag just my 2 cents.
3) You should do all of the above. I think the toughest part is getting friends to go ride with you who are interested in doing Movement Analysis. Most of my friends just want to "ride" or "ski", so they arn't really interested in stopping to take video.
Getting good video of yourself is a great way to improve your technique.