Of course. Any officer or enlisted is ALWAYS "on orders" of one kind or another, even if they are "standing orders," such as in a permanent duty station.
As commander in chief, he can issue executive orders to make changes to military protocol itself
An act issued in 1867 that forced Andrew Johnson to issue military orders through the general of the army (then Ulysses S. Grant) instead of directly to the south.
Unless you are in a very senior position you don't question military orders.
Navy Regulations, Chapter 10, Paragraph1039
Active Duty Operational Support orders
Religious orders like the Knights Hospitallers provided medical care to pilgrims, knights, and soldiers during the Crusades. The Knights Templar were a military order that protected pilgrims traveling to Jerusalem. Both orders played a significant role in the military and humanitarian aspects of the Crusades.
one who carries orders or sends orders (of some type)
Standing Medical Orders
Offline orders
NO - he can not issue orders to the American people. He can issue directives to government employees about how to perform their jobs.
The President of the United States is allowed to issue executive orders without the approval of Congress. These orders however, are subject to judicial review and can be struck down if deemed unconstitutional.
bob