I agree with about everything except:
Air to air - I would always choose the 20mm MG-151/20 over the M2 as fighter vs fighter armament because of the much larger amount of damage caused on the target, a single hit from a 20mm MinenGeschoss being enough to rip an entire section of a wing apart. The 15mm MG-151 with its high velocity round (960 m/s) excellent ballistics penetration power was a very effective fighter vs fighter armament as-well. The M2 was nonetheless a very effective weapon for fighter vs fighter combat, benefitting from excellent ballistics and good penetration power. The 20mm Hispano deserves to be mentioned as-well, being a very effective fighter vs fighter armament.
I have no real argument, particularly as the German designers had to consider destruction of heavy bombers - whereas US did not really have that problem - and the M2 was more than enough for 109s and 190s. I wish the USAF had adopted 20mm prior to Korea.
As an anti bomber weapon nothing beats the 30mm MK108 MK103 though, with the MinenGeschoss it didn't take many hits to permanently down any US bomber.
Battle-rifle - The StG.44 hands down! To say it had no impact on the war is just plain wrong. The Sturmgewehr was many times the single reason some German units made it through the day alive, once saving an entire regiment from certain extinction, enabling the infantry to accomplish the otherwise impossible, punching through a USSR pincher made up of millions of russian troops. This was made possible only because of the huge firepower the StG44 provided the individual soldier.
Perhaps, but it was more a sub machine gun than a battle rifle with shorter range and stopping power - but a high rate of fire and surely the forerunner of the AK-47. Only 400,000 built and basicaaly introduced when war was lost. The M-1 came into the US inventory in 1935 and continued in service until 60's when M-14 replaced it. A better comparison is between M-2 Carbine with selective rate of fire and about same ballistics - I would pick the 44 always
This having been said the M1 Garand is definitely the runner up, with the G43 as a close third.
Bolt action rifles - the K98k hands downs because of its superior 7.92mm FMJ-BT projectile ingenious bolt design and top strength. The SMLE is the runner up and the Swiss K31 as third.
No argument, but the M-1 was simply a better battle rifle and rendered the bolt action obsolete
SMG - The MP-40 simply because it was as effective as the Thompson with the added benefit of being cheaper to produce. But in the ned its a matter of taste as the Thompson shoots faster while the MP-40 shoots slower but more accurately. It is debatable wether the .45 ACP packs a bigger punch than the 9mm Parabellum, but nomatter what both do their job well.
The M-3 was cheaper than the Mp40 - none of the above was 'accurate' with re4spect to the rifle so doesn't seem to be a factor under 100 yards with any of the above. As to punch, it isn't debatable to SOCCOM troopers who have thrown the 9mm away and replaced with the old 45. The 45 ACB continues to lead FBI one shot kill statistics... the 9mm is very far behind.
Having said that, you can carry more 9mm and easier to design magazines with more than 8 rounds and still comfortable. My personal 'bedside comforter' is a SiG 220 in .45, and next choice would be a SiG229 in .40. My wife like her 357 and the 9mm SiG is used for plinking and target practice.
LMG - MG42 MG34
Total and unqualified agreement
HMG - M2 no doubt. The MG42 MG34 both get honourable mentions here as-well though because of their huge effectiveness at laying down accurate deadly long range suppression fire, being refered to as a cannons by the Allied troops in Afrika.
Shipboard AA - The 4cm Bofors or the German 3.7cm SKC/30.
Anti Tank - The 8.8cm Kwk/Pak43 L/71 hands down, with the 7.5cm Kwk/Pak42 L/70 as a very close second, the 8.8cm Kwk36/Flak18 L/56 17 pdr sharing the third place.
IMO the Russian 7.62cm doesn't deserve a place on the list because it didn't prove effective enough from 1942 and onwards, and the US 9cm M1 3 hardly saw any service as an AT weapon during WW2.
Then you would have to strip Ta 152 from 'best fighter' contention based on same logic as well..(for the 90mm M3 - the M1 was in service in 1940) and the M3 was in action on the M36 Tank Destroyer and M-26 heavy tank in ETO as mobile AT plus longer in AA role in PTO and ETO. The ability to depress below horizon was intriduced in 1943 which made the AA version a dual AA/AT. The radar proximity fuse made it very effective for AA from 1944 forward
Medium Artillery - I'll go for the Rheinmetall 10.5cm leFH 18(M) with its excellent accuracy, long range and high RoF. The US 10.5cm M2 howitzer is the close runner up. The 8.8cm Flak18 gets an honourable mention as it proved very effective as medium artillery, and the plunging angle wasn't an issue as it depended on the firing angle.
I could argue but won't as they are very close in all respects
Heavy Artillery - The 17.3cm Kanone 18 Mörserlafette, with the US 15.5cm Long Tom as the runner up.