We tiled up to the ceiling behind the hood. The hood went up and came down a few times in the process but we wanted to make sure the space behind the hood was fully tiled--just in case we ever needed or wanted to replace our hood.

Yes, the tile should go in before the hood, and go all the way up.

I asked my tile setter what he does with people who want to just tile up to the hood. He said, "Talk them out of it."

To the ceiling, I say.