So how does the Sneak skill actually work?

If you're moving at walk speed or slower (i.e., NOT running), then EVERY encounter has a chance to not notice you unless it's facing your way?

What if your Speed is really high, so your walk speed is quick?

Does the Sneak button help at all (normally ALT) ?

And how far away are encounters checked by your sneak skill?

Oh, and what effect do Chameleon, Shadow and Invisibility have on things?