Mom has dementia and is in a rehab center. The past 2 weeks she has been paranoid that people are out to get her and that she will not make it through the night. Is this normal?

This could be consistent with the stage she is in (sorry). I'd check with her doctor about medications, both because some people can react negatively to medications (paranoia is not an unheard of side effect), and because it's possible something new could ease her symptoms.
The paranoia that often accompanies some dementias is horribly frustrating as the family sees the person's fear and pain, but also because the family is often a target of the paranoid thinking.
Do check again with the doctor. Checking for a UTI was very wise, by the way - but see if there's something more they can do.
Take care - this is a long journey,
Carol

My first thought when I saw this question was Meds. If she is taking any psyc. meds this could be the cause or like Carol wrote it may be just the stage she is in. My Mom has been off and on Meds. It takes about 30 days to take proper effect after this, if no better she may not be on the right meds for her. Also comming off psyc meds will make her unstable. My Mom was really paranoid and I later found out the aid was letting her watch CSI. Combos of Meds my make her react this way as well.
Speak to her DR and psyc. Dr to get clear on her behavior and why shes on certain meds. You really need to be aware of stages and side effect so you can understand why shes behaving in certain ways. I have a friend who cared for her Mom ... she had a painting of a girl in the hallway ...her Mom yelled at the girl in the painting to get out of the house. My friend took painting down, end of that problem but not always so easy. Most people don't know this but depth perception is altered when someone has dementia in some cases so things don't look the same anymore to them. Stairs look like they are flat for example.

My Mom does not have Alz, but still had the same reaction as your Mom when she was in rehab. She was recovering from a painful injury in her shoulder and they gave her Vicoden. She called me in the middle of the night and told me that one of the nurses was trying to kill her. I had them reduce the tablet to half, then had them take her off of it and give her tylenol. The doctor who gave her the meds would not admit that this was causing the hallucinations and odd behavior. When she was off of it, her normal personality returned.
Make sure that they are not giving her meds just to "keep her quiet."

Thank you for your answers. We will look into the meds.