In answer to the question "did I play the hand good?"
Blunt answer, in my humble opinion, no.
Alright. If you're gonna play K-J against a short stack, OOP, don't donk bet (lead into the raiser). It's going to be very difficult to know where we stand when we take this line.
As played, what is the question? Call the turn shove. It's automatic in this spot you created.
Sure we can call preflop, and I don't mind it here to be honest. But also beware that KJ is going to be dominated a bunch. If you want to play it, against a short stack, OOP (the hard way), then be prepared to not know where you are, possibly be crushed by a better hand, etc.
But when we hit the flop, donk betting is just so horrible in this spot. You are building a pot, and you have no clue what V has. I hate leading the flop here. Villains range will seem super wide, because he is calling almost always. But if we check, maybe he bets, we call. Turn goes check-check. Ahhh, now we have something. A little piece of the puzzle, to help us narrow down his range of hands.
We don't need to be bloating this pot. That's what donk betting does, it makes the pot get bigger, hence the inevitable turn spot where dude jams, and now, his shove will make you "2nd guess yourself". Probably because you have no effing clue what he has, because you are OOP, with a mediocre hand.
Check, and call when villain bets. You get added bonus of also seeing what the other villain does before you act.
However, because you chose to call this raise with a hand like KJ, you also have to deal with the consequences of not knowing if the shit is good, or not good. This hand would play much better if we flop a straight, straight draw, or 2p (obv). Check calling in this spot is probably more effective of getting value from hands we beat.
But all in all, this guy doesn't even have any money. Just check call, get it in, whatever. It's not a tough spot (as played).
And maybe I'm a nit, but I don't think we have to give this dude action with KJ. We could just wait. I hate giving people action, that have no money. I despise short stackers. They contaminate my cardroom every day, and I never give them action, unless I am playing monster hands, and stacking them. It's just not worth the risk. There nothing to win.
I think I remember you saying buy in is 50BB (in other threads) so I'm aware of that dynamic. Still, you have a decent stack, don't double this dude up, if you can avoid it. Just whack him later, with better cards, position, etc.
So that being said, I don't mind a fold preflop either. Take the $0.02 bro.