1) It’s kinda weird but also sort-of understandable if you keep reading the following panels. Endeavor outright states he doesn’t want Natsuo to forgive him. Endeavor was afraid that if he saved Natsuo, then Natsuo wouldn’t be as against him anymore, not necessarily because he forgives, but because he’d owe him at least being civil and stop antagonizing him so much. And Endeavor doesn’t want that. Or that’s how I understand it. Doesn’t make it any less weird and yeah, he still should have saved his kid anyway, but there are times when even the best of pros are overhwelmed by emotions.
2) I strongly disagree with the entirety of this point. First of all, what Endeavor says doesn’t, in any way, imply he blames Touya. On the contrary, he blames himself. This line implies he isn’t directly responsible, meaning that if Touya died, say, because of stab wounds, Endeavor wasn’t the one who did the stabbing. BUT! We don’t know how Touya actually died. (Or if he died at all considering the Dabi theory, but that’s beside the point.) It might have been over-training or a consequence of that, but it might have also been a villain attack or a number of other things. What Endeavor says basically implies, even means, that while he isn’t responsible for Touya’s death logically and (most likely) legally speaking, and he logically knows that, he blames himself anyway. So it is a strong statement of responsibility, because he’s taking blame for something that in actuality wasn’t his (direct) doing.
Second of all, how is it ego-centric? Like, yes, ok, he feels guilty ‘without taking responsibility’, but he also admits that ‘all he could do was blame others and dodge responsibility’. He admits his faults. It’s pretty obvious he’s not proud of it. And he’s trying to repent now. To the point that he’s willing to let his kids and their mother move into a new house without him, to remove himself from their lives entirely. Is he late in taking responsibility? Well, if Touya is dead or a villain (Dabi) then yes, probably, but at least he’s trying. He’s changing and he’s looking at the bigger picture, at what’s best for his family, whether that includes him or not.
For the record, I’m not a fan of Endeavor or anything and I’m not trying to defend him. I don’t really like the guy and I don’t think I ever will. But I do appreciate how Horikoshi is handling his redemption arc. And I try to give the guy some minor credit where it is due.
3) That’s not present tense. Present tense would be ‘Touya tells me everything’. This is present perfect, which is still a past tense and means that whatever is being referred to is in the past, over and done with, it’s not happening anymore. So I doubt Natsuo actually still has any form of contact with his possibly dead brother.