Reminder that a crossbow will absolutely go through kevlar. It's also quiet. Given the shooters other actions I doubt either of these thoughts crossed his mind despite ultimately getting into a shootout with cops where that kind of penetration might matter.
Absolutely this. .22 LR will kill a man just fine, Mossad's favorite weapon was a .22 Beretta (best ammo availability worldwide and one of the better options for use in airplanes, among other reasons), but getting rounds through the door at all is questionable, it really depends on the door (I know some of the interior doors in my house probably wouldn't stop a .22LR), much less getting rounds through the door with any accuracy or consistent killing power...and have fun getting hit with shrapnel from your bullets if you stand too close to the metal bits like doorknobs if you try to "shoot through" them with one. Happened to someone I know when they decided the easiest way to put a hole in some metal was to use his .22 pistol at close range when they were young and dumb.