Starting from the last part: A huge part of the nonmilitary support services for the services are done by civilian employees of the Federal Government, or by contractors. For instance, the teachers at the on-base schools are civilian employees of a “School District” made up of the schools in the bases of that geographic region. Example: the Antilles School District employs the teachers at the schools for the children of personnel deployed to Ft. Buchanan, the Point Borinquen CGAS and the San Juan CG Station (and until they closed 3 years ago used to do so for the Roosevelt Roads and Sabana Seca Naval Stations). Use of civilian employees and contractors is ever more frequent in the current day, as the call is to have the trained soldiers (sailors, airmen, Marines, coasties) do the work of trained soldiers (etc.).
As for the first question: I could be snarky and say, Chairman of the Joint Chiefs of Staff. Nobody is gonna put General Pace in a position to fight his own way out of anything except maybe a budget hearing
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But, seriously, as mentioned the Chaplain will not ordered to grab a weapon and take the line (though he may “praise God and pass the ammunition”). And the direct-commissioned Physician/Nurse or JAG lawyer, who do not get the full course of Basic Training, will not be routinely armed, though they may be issued a sidearm from the armory if the CO deems it appropriate for self-defense – anyway your MDs and Nurses are too valuable to risk in a shootout.
But the chaplain CAN be right behind the line, ministering under fire, same for a physician at the Field Hospital. And the JAG, unless he never leaves the Division HQ bunker, is as vulnerable to an IED as anyone else. Of course, if you’re Navy or Coast Guard afloat, everyone in the ship gets wet if it goes down…
A the Army enlisted personnel contracts do all stipulate that besides your specialty MOS, if necessary you will be called up to engage in the type of combat activity for which you got Basic Combat Training – things like defend the perimeter of your camp, if your frontline becomes flanked. George Patton famously called for the clerks and cooks to grab their weapons step into the line during the Battle fo the Bulge, when the infantry was stretched thin.
The military alternates your deployments so you get a mix of locations and unit assignments. If your MOS is Computer Geek, part of your enlistment may be setting up systems at a training facility in California, but your next billet may be systems maintenace for a deployed Armored Brigade, having to go out to Batallion HQs to fix malfunctions – and if it so happens that 2nd Batallion HQ is outside Fallujah… well…