Is it possible my ex could get me fired?

All you can really do is keep living your life as a respectable person. You may want to speak with your boss and inform them of the situation. If he ever tries to get your child taken away I can pretty much guarantee it won't happen. In those situations they always look at the past history of the person. If the history shows that you've held a job for a long time and have never gotten in trouble you won't have anything to worry about. As for him lying to the police, they probably won't take him seriously. You shouldn't worry about that. If he ever threatens you in an email, text, or voice mail make sure to save it, just in case.