Harry Potter and the Philosopher's Stone?

I have already read all 7 HP books, but I'm re-reading them because this time, I know how it ends and why people acted the way they did. But I'm still not clear on one part in the Philosopher's Stone. Why was Snape trying to steal the stone? And when he asked Quirrell to remember where his loyalties were, didn't Voldemort hear him? Because in the later books, Voldemort believes Snape is on the Dark side...