1.Well some games ask you if you have laready done Alpha/Beta test, so it can be a way to choose your Beta testers based on their experiences.
2.This is totally false, it depends mainly of the NDA of the game/Devellopers. Some allows Streaming, Youtube etc... during even the alpha stage, Others don't. We just have to know Greybox/Yager's rules about it.
You may be true, I'm simply stating my overall experiences with the beta information I have seen in the past few years :]