I totally get what you mean but I do think a little differently. To the first thing, I think he didn't go to his parents because they thought he was dead and it's probably a lot too handle when they find out what he had to go through. Being an assassin may just kill him some day and if his parents knew that he is alive and then find put that he's dead or sth like that it would just make them feel the pain twice. He could also just want to leave his "past live" behind because he created a new person by being black swan. Or maybe they're already dead, who knows lol.
To the second thing, the mafia dude already said that he liked him since the beginning and that he loves the way the mc is so I don't think that he will ever have a problem with it because he loves him for it and the mc also liked that the mafia dude has nothing against him. It's just how he is so he can't and shouldn't change that. That's why I think that they actually will stay together for a long time. They also said that at the end of the day the mc will come back and be his lover.
But like I said, I get were you're coming from so I don't mean anything in a bad way!
I have a few things to say about this
First, why didn't we get a glimpse of his parents? Sure they think he's dead but it's not like he couldn’t meet them even if they think he's already dead, I'm sure they would’ve been happy to get to know him (maybe they're dead too but there wasn’t a single clue that indicated this outcome).
Second, their relationship might be fun now, kinds like the dynamic of cats chasing rats but it really feels like it wouldn't last long.
Overall the story was a bit fun but idk at the end I felt like "meh"