Harassing emails and texts are becoming quite common as an incident of divorce. His accusations are just that, accusations, until you respond. I would suggest you keep records of all these accusations and if the time comes and you need to refute their suggestions before a Court of Law, with the help of an experienced attorney, refute them then. Anything nasty or disrespectful you respond may be used against you so it is better to avoid making a record.
Contact an experienced family attorney if you need assistance in getting the Court to restrain his harassment.