Is it ok to sleep on my back in late pregnancy?

No. It is best not to sleep on your back. Tilted to one side or the other is best, usually propped with a pillow or beach towel folded lengthwise a couple times. The "lazy-boy" position is also ok when it is hard to get comfortable in bed. These positions help with better blood flow to the uterus and also with swelling.
Sure. As long as you are comfortable, it is fine. Most women find it difficult. Good luck with your delivery.