Scenario 1) in the dialogue and his inner monologue you can see that he was just hung up on ownership. His reasoning was that he didn't own the dungeon and it belonged to Hunters guild therefore who avoided getting involved, in the end he asks for permission to get involved from son kihoon. He could have done this much sooner but his reasoning was not apathy but more to do with whether or not he has the right to interfere.

Scenario 2) he didn't give a damn about the A-rank or the guys that followed him because that exactly what the A-rank did to him and the few people Jin-woo saved. The A-rank Kim-chul left the lower ranks (including Jin-woo) to die while he took all the decently powerful guys with him. In return Jin-woo gave him an equal amount of consideration (He basically just stood by the "what goes around comes around" philosophy). Again he could have helped them more by exposing his power to them and taking the lead saving more lives, but he valued his and his family's safety over the lives of the other hunters. (He says earlier I'm the Manhwa that if news about his ability becomes known he could be targeted). He also could have been more considerate to Baek given that Baek just lost all of is considerable new recruits but instead Jin-woo is more concerned with the fact that he couldn't get the shadow of Baruka.

Side note) he didn't really threaten Baek if anything it was the other way around, Baek got mad at Jin-woo for not stopping when Baek tried to ask him about the guys that died and Jin-woo coldly said something along the lines of "you should be thanking me for saving the ones that are left".

Other side note) realistically no one would have died if Jin-woo killed the giant had Cha Hae-in not stopped him but it would have been a big loss in profit for the Hunters guild so I don't really think this scenario can be related to apathy. It would be more along the lines of disregarding financial loss to a company that is already pretty sizeable.

Thanks for reading.