Well you have to remember we didn't start fielding units with all Garands until 1943-44. If you look at early footage, especialy in the Pacific 1903's were still the norm.
The fact that the basic structure of the Garand is still alive and well today in the form of the M14 speaks for itself.
Yes the German style of fighting based around a machine gun, we stole that from them after the war. Good idea!
The BAR couldn't lay down nearly the same fire as an MG34/42. I understand they prefered to use the BAR's in groups of 2-3 so that one was always firing.