The movie was surprisingly accurate except for a few minor details. He had more siblings than the movie showed, he used a 1917 Enfield rather than a Springfield and a .45 auto rather than a captured Luger.
I think they purposely changed the pistol because York was violating some regulation by having the .45 and he didn't want that to be shown.
No, Corporal York was an NCO. He was ISSUED his 45 auto.