I'm guessing that the dad was homophobic and discovered his son was engaging in some sort of same sex activity. (Probably something minor like hand holding or a kiss given their ages too). There was another manga too where the mum ended up collapsing and has spent years confined to a hospital simply when her son came out to her, so the trope of a parent dying or suffering poor health over something as mundane as having a gay kid isn't unusual. I guess the dad was one of those people that thought he had failed as a parent, and his child had brought shame on him or something to the extent where he could no longer continue living.
Well, it's just as you've said, the father found out that maybe Seokjo has a crush on the MC, after all in the flashback that was shown in Chapter 5 that Seokjo admitted that he was involved on that suicide incident.
Then, about the injured hand of the MC, it was also included in the flashback (Chapter 5) that Seokjo will always look at the MC's right hand when he was fighting or talking to the girl childhood friend. Well, after all he's using his right hand to hit or err pinch(not sure) the girl. So maybe he was just jealous. Or maybe there's more to that? But maybe it's part of the reason? It's a guess though.

I feel like his dad sexually assaulted the MC and in the hammer time guy's mind it's the MC's fault his dad killed himself cause maybe he told someone he was assaulted and the dad wanted to get out of trouble, so hammer time blamed and took a hammer to MC's hand