I am 14 weeks pregnant and need a chest x-ray. Is it safer to wait until 20 weeks gestation or is the risk the same if I do the X-ray now?

Now is fine. Your baby will be covered with a lead apron over your belly when you get your chest x-ray. If you need to have an evaluation, earlier is better. Appropriate precautions for the baby will be taken.
It depends. If your doctor is checking for an acute process such as pneumonia, the technologist will shield your abdomen and pelvis. A non-emergency exam could be delayed.