What does God do when we fast? Do the gates of heaven open wider when we fast? Do our hearts come nearer to the central Glory when we fast? Does God really work on behalf of those who fast?

I think a certain level of hunger makes the mind think more clearly. It also positions the spirit to a more sensitive state as to receive spiritual dealings. Symbolically, it also stands for a healthy degree of detachment from the material world. To be able to attach to the spiritual world, going hungry by and itself does not make one more godly.