In WWII my father was a glider pilot (warrant officer rank) assigned to fly in the 82nd airborne glider infantry on D-Day. He was equipped with a "grease gun" which I believe was a .45 cal submachine gun. The paratroopers in the first picture appear to have the same type knife that my father called a "survival knife" attached to their boots.

For the M1A1 carbine with a folding stock in the movies check out "Objective Burma" (1944) starring Errol Flynn as Captain Nelson who humps one of those through the jungle.