you're a lot better than i was at the same age.

the sherman was the US army's main tank. it was classed as a medium tank but the notion of a "main battle tank" then was vague.

the main battle rifle was the garand. the carbine was a self-protection weapon, basically for behind the lines though some army men preferred them for jungle fighting over the garand.

the HMG would be the browning .50 cal while the .30 cal would be your LMG. the BAR was the BAR.

as far as europe is concerned, you hit the fighters on the button, for the US that is.

the (heavy) bombers were b-17, b-24 and b-29

you got all the germans right save for the fighters.

the russian, japanese and british are basically correct.