I think that light misting might be beneficial to your tree. As for encouraging new growth, I haven't got a clue. I am glad that your tree is recovering!

No, pruning won't help now, but if the branches are truly dead, you could prune them off. You could try thread grafting - http://www.bonsai4me.com/AdvTech/ATthreadgrafting.htm.

These trees are typically sold for beginners, but they are anything but a tree for beginners. I sold one a few years ago and got a call the next weekend, "This tree you sold me is dead!" Well, of course, he dribbled a little water on it on Friday, and left it in his office all weekend. It dried up immediately.

I have seen brush cherries die from too little and too much water, and they usually die on one side first. Your dry branches are probably dead, but don't cut them off too soon. Wait until you know they are dead: i.e., brittle with no green under the surface.

Good luck to you.