They are interconnected, parallel dimensions that depend on each other and cannot exist separately. That connection is the reason why there's a balance in the Universe. Unfortunately, in my opinion, that is never explained in the game. That balance is thrown off in DmC when the demons decide to take over that dimension. Why haven't the angels intervened, given that this would affect their dimension as well, it is not explained.
Yes, every time Limbo changes to attack Dante there's an effect in the real world.
Limbo was always seen as a living organism, not just buildings and streets. I think part of the reason to give it a voice was so it had a bit more character to it.
Yes, there was the discussion of making platforming less linear, but it was largely ignored. That section in particular was extensively simplified and redone fairly late in the project because testers were constantly getting lost. I could get into details about that particular layout, but there is a bigger discussion to be had in terms of designers overreacting to testers not finding the correct path within seconds of entering an area. Many modern games are devoid of a real sense of exploration and discovery, in my opinion.