It is very possible for a JW to be homeless/transient. They strongly discourage careers and education, just wait for the Sky Daddy to take care of you.
The head shaving has nothing to do with JW. In fact, she will probably be counseled by the church elders for doing that because it draws attention to herself. (Sometimes homeless folks will shave their heads because of lice they got from sleeping in infested bedding.)
JW do not believe in psychiatric help or mental illness. She would be looked down upon for having a mental illness and more so for getting treatment.
jw do not date w/o chaperones. She would get in trouble for being alone with you. The fact that you are a non-jw means she would get in deeper trouble.
This woman has a lot of problems.