As the idea stands for nation division: Japan/Germany/Italy England/Russia America
Map rotaion will be every six weeks (one week equals one year)
Based on the criticisms I've seen I think I've thought of a few ways to balance things out and fix problems:
1) American air would dominate because the other sides lack good heavy bombers
A1) Add planes:
HE-111
DO-17
HE-177
DO-217
Handley Page Halifax
Short Stirling
Bristol Beufighter
The He111, Do17, Stirling and Beaufighter (a fighter-bomber, not a bomber, FYI) would do nothing at all for balance in this category. The Halifax is essentially identical in capability to the Lancaster and so adds nothing. The Do217 (and Ju188 that you didn't mention) are good solid medium bombers and the He177 is a wildcard, but likely a decent heavy bomber. Conclusion: The British and Russians are just as doomed as they were before. The Germans, Italians and Japanese situation has improved.
A2) Larger formations (i.e. 5 planes) of medium bombers
A3)Limit the number of heavy bombers that a person can use
Because these would affect all sides it does not change the balance.
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2)England/Russia lack esscort fighters
A1) Add Planes:
Boulton Paul defiant
Westland Whirlwind
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I have no idea why you would suggest either of those as escort fighters. They are both short ranged and poor performing early war fighters. The Defiant in particular would be helpless to defend itself let alone anything else. The only things you would really add here would be the Mosquito Mk 30 and perhaps the Yak-9D, though the the -9D still only had 845 miles of range. While the Mosquito Mk 30 was a good twin engined, high altitude fighter, I wouldn't care to tangle with Bf109Ks, P-47Ns and Ta152s with it too much.
3)America will dominate the seas
A1)Add planes:
Fairey Firefly
Fairey Swordfish
HE-115
The Firefly would be helpful to the British/Russians, but the Swordfish would be neigh useless with the B5N2 being vastly superior. They still would still urgently need the Seafire L.Mk III and, if you want to loosen the rules, Seafire Mk XV. The Axis get absolutely nothing out of the He115 as it would be nothing more than a flying target. The B7A2 and D4Y would give the Axis more comparable strike aircraft but nothing can be done for them fighterwise unless the rules are grossly loosened and the A7M2 added (good luck on getting accurate performance data for the A7M2).
As we are done with the plane section of your post I'll add the note that you do not seem to have any idea what many of the aircraft you are naming actually are.
A2) Add more ships/AA to lacking nations
As long as historical guns and ships are used nothing can be done to help the Axis here. Without proximity fuses, which they never had, their defenses will be weak. The British would bring the proximity fuses to their side (they were am American and Canadian development).
4)People will not like that they are forced to fly certain planes
A1)The arenas will be set-up like this:
WW1
Latewar MA
Evolution arena
Help/Training
Dualing
Axis Vs Allies
Special Event
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Without more description I annot comment on this.
You also left out the bit about the Axis utterly dominating on the ground. The British Germans are so-so on tanks with the Sherman VC 'Firefly' and T-34/85, but completely lack any AA vehicle. The Americans are doomed with only the M4A3(75) and M4A3(76) for tanks and weak in AA with the M16. The Axis Panther V G, Tiger I and especially Tiger II would be nigh unstoppable. Wirbelwinds and Ostwinds as AA vehicles just rubs salt in the wounds.
