Is weight-lifting safe in pregnancy?

It can be. If you've never lifted before review this with your OB and consider working with a certified personal training who has worked with pregnant women. If you've been resistance training consistently in the past, it's not unreasonable to continue - though you may want to take it easy on the intensity level - during your pregnancy. If you have any complication during your pregnancy, review with your OB.
Possibly. It is safe if done correctly and approved by your obstetrician. There are many exercises that are safe to perform right up to delivery. Check first with you doctor!
Yes, in most cases. In low risk pregnancies light weightlifting is safe. I recommend no prolonged exercise on your back. Use common sense and if it hurts do not continue. If you have a high risk pregnancy, check with your doctor first.