Short, and to the point; very concise and easy to understand. Just a couple of minor nitpicks.
The invincibility on Up smash is frames 1-4, not frames 1-5 (though I wish it was 1-5; that extra frame can make all the difference).
Up air does actually hit behind him. The hitbox is out frame 7 as he begins to move his head forward for frames 8 and 9. Interesting thing to note is that up air has less landing lag (12 frames) than nair (13 frames). High damage output combined with low base knockback and low landing lag makes falling up air a good combo starter at early percentages since it won't knock the opponent very far away, but will put them in enough hitstun for you to follow up with something else. At 0% it's even possible to follow up with a grab if the opponent doesn't immediately jump away.