Her hands looked completely free when she got out of the elevator. I know some people think she put one on her back, but... Not exactly practical (not even sure she'd be able to reach around with those arms, either).
As for the egg sack accelerating anything, we see what the eggs look like inside it when Ripley shoots it open. They're at very primitive stages of development. At the slow rate she's laying them, it looks like it would take a long while for them to 'mature'.
It's OK to hand-wave it away, because that's the only way 'Alien 3' can possibly work, but it's still pretty much an anomaly, logic-wise.