I wouldn't immediately judge a woman as not being pregnant based on what she puts on Facebook. While there are women who will happily post for the public to read every detail of their cervical mucus, abdominal bloat, conception date, and all the photos from ultrasounds (including their names), there are also creeps out there who get off on photos of pregnant women, people who steal identities, old boyfriends who are vindictive, and all kinds of other reasons a woman might not put such information out online where just anyone could see it. It is hard to judge whether someone against whom you had to take out a restraining order is in the first category or the second, but just the absence of mention of pregnancy on Facebook doesn't mean the absence of pregnancy.
Your boyfriend could put it to the test by asking to go to her doctor's appointment with her, or I guess because of the restraining order he could ask if some relative of his could go with her, like his mom or his aunt or his sister. If she's sure he is the dad and has nothing to hide, she would be glad to have someone like that come along, so she can show she is telling the truth. If she refuses, it suggests that the whole thing is made up more strongly than her Facebook posts.
If this idea gets nowhere with her, all your boyfriend can do is tell her that he will see her for the DNA test when the baby is born, and continue with the restraining order in the meantime. I'm sorry that you are still living where she knows where you are. I'd consider moving as soon as the lease is up. Good luck.