Hearing is more involved than taking sensory input from two sources. If it weren't, there wouldn't be mixing and mastering engineers using speakers. Which they mainly do.
Pretty sure they use speakers because they are mastering primarily for speaker setups. Not because it increases the accuracy of location information encoded in the sound.
Nope. Because headphones don't give you sound pressure fluctuations in your body, and because the depth (not width!) perception is all messed up when using headphones.
Yeah, it's a lot better than without the transfer function. It just doesn't react to my head movements, which speakers do (by staying stationary relative to my head)