The officer says he "gunned" Mike at 4 MPH as he went past the stop sign. Speed guns used by police use either radar or laser, and only return a reading when a vehicle is approaching or going away from the officer's position. In this case, the officer was on a side street at a 90 degree angle, so it would have been impossible for the officer to obtain a speed via a speed gun.
Eve asks the officer if the state traffic law 107 trumps the 1st Amendment, and the officer says it does. The US Constitution has a supremacy clause that places it above any other law, so the officer was incorrect. The fact his answer contained the phrase "lawful order" means the order given would have to be lawful. In this instance, it was not as pursuant to the 1st Amendment citizens are able to protest on public property, to include alerting motorists about speed traps. Any order given by an officer to prevent them from doing so would be unlawful.