Trooper
Shooter
Probably not when they're acting as part of the military, but their peacetime home is now under Homeland Security.
The PCA only covers the Army. And because the AF came out of the Army then they are under it as well.
As the PCA is an act of congress, congress can grant the Army additional powers and responsibilities. At one time the primary LE force for the federal government was the Army. Even to this day all federal LE powers are based on the authority of an Army officer to enforce federal law.
Basically the Army got too heavy handed after the Civil War and the congress decided to restrict them. Also to limit the local sheriff from making the local soldiers part of his posse.