As the other answers have said, the answer to the first part of the question is yes. You lift him 10 feet, he falls 10 feet, and takes the usual damage.
For the second part, I would consider vertical movement to follow the same measurement rules as horizontal. If you are playing on a grid, two 5' squares diagonally is still measured as 10'. So at a 45 degree angle, the fall distance will still be 10'.