Is it safe to do resistance training while pregnant?

Yes. It is ok to do resistance training while pregnant as long as you do not "valsalva" while doing it. "valsalva"ing is when you hold your breathe while straining like you are forcing a bowel movement. It can increase pressure in the abdominal contents i.E the uterus.
Yes. Walking is resistance training against gravity. So is yoga and pilates. So you can do highly effective resistance training without a lot of equipment. Start slow and work up the resistance gradually.