@Navalland Like the work that you are doing. Here are my opinions to your questions,
I would rather play on a World version simply because it is more. I am always a fan of more so given the choice between Europe or Europe + everything else I will pick Europe + everything else. That does not mean that I always need to have a World map, I am just fine with a Europe map if that’s all there is. Additionally, this is your map, not mine. If you are good with just Europe then there is no need to add more.
If you are making a Europe map I would recommend at least adding some connection from the Atlantic to the Middle East area (to represent sailing down under Africa) as that route was really important in moving soldiers to maintain the Middle East and North Africa fronts.
It is a hard thing to try and make the US go on both sides. You can try to balance it to where if the US spends too much on one side and too little on the other that the other side is going to win. To where the US has to spend so much on both sides to prevent one side from winning. Of course this would work only if all players knew what they were doing and would work less with beginners.
Alternatively, here is my better solution. You could split the US economy between the two sides. The US income from these territories go towards Europe. The US income from these territories go towards Pacific. The income collected on the Europe side has to go to the Europe side. The income collected on the Pacific side has to go to the Pacific side. The US is allowed to move units from one side to the other, but at a cost as to discourage having a massive army on one side while still allowing the US to have the ability to have more units on a side if need be.