Psychotic disorders?

should people with a psychotic disorder watch small children alone

You can't be too rigid on this one.
Of course, someone who is psychotic should not be left to care for small children. But someone who "has" a psychotic disorder, that's a completely different thing. They might be medicated and not have had an episode for months or years, but they're still described as having that disorder.
For example, my wife is bipolar I. That's classified as a psychotic disorder. However, she is medicated and functioning normally. we have a son and she is alone with him lots. I can't watch her all the time, and anyway, I don't want to.
So the answer is "it depends."
Most importantly, It depends on whether the person is legally a custodian of the child (ie it's their child) or whether they are considered to be a danger to themselves and/or others.
Sure, be careful, but don't make problems where none exist.

NO WAY

I don't...think so.

Have you ever had thoughts of hurting children or ever hurt people period. If so you can't help a child when you can't help your self.

Generally, I would say no, but it really depends on the person. If the individual is doing well on medication, or the disorder is in remission, it might be okay. I have a friend who has schizophrenia, but she's doing well, and she takes care of her grandchildren without any problems.

If they are contolled with medication and psychotherapy then yes!!

It depends on how bad it is... people always say it sounds bad but I am diagnosed with a 'psychotic disorder' and I babysit, go to school, and it doesnt affect my daily life. Figure out if the person ever loses complete control.