Not 100% true. It takes an act of Congress, after the shutdown is over, to retroactively give them back pay. Which then the President has to sign.
Up to now, that has been the case. But it's not a guarantee.
But it’s not a guarantee.
True but if they don’t pay the troops they can expect law suits form every employee organization and union. Not to mention lots of damage to equipment, computers, and who knows what all.