Did Kid NOT kill his dad on PURPOSE?

In a word, no.

The Kid wasn't good enough to both outdraw Herod and place a shot that would merely disable him as opposed to killing him.

The Kid wasn't even sure he was going to win that fight anyway. He spent the last minute before the draw trying to convince himself he was going to win by trying to convince the crowd. If he was sure of winning, what purpose would there be telling the crowd that Herod was not invincible if not to convince himself of that, or even perhaps placing a seed of doubt in Herod's mind?

No, it was a fight to the death and like it or not, the Kid was trying to kill his father. In this sense anyway, he was no better than Herod.

Is very bad to steal Jobu's rum. Is very bad.

Well remember that at that point the duels were to the death. He couldn't just shoot him and put him on the ground, he had to kill him in order to win.

You kinda got a spoiler in your heading.

~ the hardest thing in this world... is to live in it ~

I think he truly lost. I don't think his shot was off intentionally.

You're not going to place many shots in the upper body of a human being without seriously risking death. The kid grazing Herod in the neck doesn't exactly seem like a purposely missed shot to me.

Had Herod been hit in the arm or the leg I might believe it but the kid would still have to know that Herod would likely go for the kill shot himself and understand that while it might impress him to wound him on a quick draw that he'd ultimately pay for his gesture with his life.

It was a duel

I think the kid actually won the dual and intentionally missed. Herod didn't want to kill him. But when the shot went off and he was hit, his reflexes kicked in and he went for the kill automatically.