as far as the flop goes, first of all, we are going to be getting folded to a huge amount of the time. vs more aware players this is often an argument for betting our whole range smaller, because our range is going to be so bluff-heavy (obviously in response to their high fold %) and so we want to give ourselves a better price on our bluffs. however i imagine this guy's range is probably pretty static vs different sizes. assuming he's probably some fit or fold fish who doesn't hand read, he's either got a hand he wants to play, or he's already folded in his mind and wants to see his next couple of cards. i doubt there are many sizes < pot which influence his calling range until we get really low, like $1 or less. bearint this is mind i think your sizing is fine and you could perhaps have even gone $2 or $2.25 because of the above reasoning and it makes it easier to get stacks in.

on the river i guess it's a matter of weighing up the value of betting smaller and have 9x call at a greater frequency, or shoving and getting it all the times he has Kx. without bothering to do the maths behind it, i'm pretty confident shoving would be correct. though if someone wants to refute that and show my why it's not the case i'll gladly change my tune.