I'm wondering the same thing. Posting to keep up with your responses.

How high depends on several things, like how wide is the hood.

I would tile first so if the hood is replaced, there is less chance of a mismatch.

Check the cooktop manufacturer specs on venting height. They will give you a height range. Also be sure to take into account the height of all cooks...while my wife is fine with a vent at 30" I need it no less than 34" so that I don't bang my head when flipping pancakes! And yes, the backsplash tiling should go in first!

I put my backsplash in after the hood, but I have an under cabinet mount hood not one of those giant industrial kid...not sure if that makes a difference. And mine looks great. Just check the specs for height placement. A good tile person will make it look great.