You wouldn't get speeds any faster than you would with, say, fiber optics, since you still have to send classical information down a classical channel in addition to the quantum information that gets sent by entanglement.
No, not checksummable. Random. The correlation is that if you know what one end's state ended up as, you know what the other end's state is. But you can't pick the state. So it's a pair of geographically separated random sources with high correlation.