When I do the knee extension to a full stretch, even with minimal weight, my knees make the most awful noises, and also hurt (with sharp pains). If I don't go all the way, my knees are noisy, but don't hurt. So should I persevere with the full stretch, or would I be better off not trying to stretch completely?

First, I want to remind you that I'm not a medical doctor. I hope you will discuss your knee symptoms with your physician and follow his or her recommendations. In the meantime, I suggest you do the exercises with reduced weight (maybe even use no weight) and through a reduced range of motion - whatever it takes for you to do the exercises without pain. Don't worry about the noises, but do avoid pain. Then progress slowly, cautiously increasing both the range of motion and the amount of weight you're lifting. Over time, you should be able to strengthen your legs and improve your flexibility.