No, sand generators are not allowed. Anything that gives you something for nothing or that exploits a glitch isn't acceptable. Although, things like obsidian, cobble, and stone generators are, since they all use an intended game feature.
No, as it gives you items in an unlegit way. The only thing that gives items in an unlegit way that is allowed is redstone obsidian generators, as it take the redstone away from you, and gives you obsidian.
Don't forget string powered obsidian generators. (I usually try to refrain from correcting/adding on to people, but I just couldn't help it this time.) No problem, and thanks for asking first!
