The question highlights a common misconception as to what executive orders are. Executive orders are not regulations, rules or laws. Executive orders are a performance of the office as the chief law enforcer. With that in mind, what Executive orders are issued is to concentrate resources on enforcement existing laws or to remove resources from enforcing existing laws.
An executive order cannot be issued in connection to laws that do not exist. For example, your question implies that a President can send out law enforcement to arrest people who violate some non-existent law that the President thinks up. Once the police arrest you and get you to go to court, there has to be a law that the arrestee violated. If the law does not exist, the judge will just sit there unable to inflict punishment.
So the answer is No because there is no path for the President to make any law with punishment.
That being said, there are bureaucracies that do exist that can make their own rules, exist outside presidential and congressional support and have teeth given to them by congress. That is the executive branch bureaucracies such as the EPA, FCC, USDA, etc. They can certainly eat away at the first amendment and have. If you worry about losing first amendment rights, that is where abuses are rampant.