Do executive orders actually apply outside of the Executive Branch? I did not think that they did.
They are not supposed to. Not on any level fed./state/local.
No, they don't but the his orders to the agencies of the executive branch can a big impact on you...think DOJ, FBI, IRS, etc depending on how they implement what they want to implement. They can lawfare you to death or they can freeze and confiscate assets. You'll have to fight them to get them back, and you won't have anything left if you do win.