Yes, it's OK to drive without the rear shaft. Just put it in 4 high. The steering will feel funny, but that's all.

But before doing anything, check on the warranty situation.

I can't think of anything that would cause a whine sensitive to steering input AND power application. Could be two separate problems, or else I'm missing something. A whine when steering is usually low juice in the power steering pump, a bad pump, or a loose drive belt.