Hi, I'd like to help you with your question.
From what you said, you are concerned that your ex partner has been accusing others of certain behaviors and you want to know if he is capable of the same behavior he is accusing others of.
With Schizophrenia, paranoid delusions cause the person afflicted to believe others are trying to harm them. However, only one in 10,000 people who are diagnosed with a mental health disorder are actually dangerous. The key to knowing if your ex partner may become dangerous is to understand his personality away from his disorder. Was he a violent person prior to being diagnosed or is he that way when he is not suffering from symptoms of his disorder? Also, if he has a delusion and he becomes part of that delusion, he make act out on it.
However, predicting if he will become violent is much like predicting if someone without a diagnosis will become violent. Many factors go into determining a person's potential for violence and as you can tell from the news, many people are unable to predict someone else's behavior no matter how well they know them.
If you are feeling unsafe having your children with him, I would recommend supervised visits if possible. It does not necessarily have to be you that supervises, but another adult is fine. Also, visits in public areas help as well. Anyway you can set it up where you feel safer is the best bet.
I hope this helps you.
My best to you,