1) It wasn't his daughter. His daughter got killed at the start of the game / infection outbreak by the army guy.
2) No, he wasn't right. Again, not his daughter, but a "delivery" that was supposed to cure the infection and save the world. He made the wrong choice and caused the infection to spread, countless people die, as well as the wars and fighting of the desperate trying to survive.
3) Of course, if I had developed a bond with a kid over the course of the journey, I can't say I would've done the right thing either, but that's the point. 1 kids life vs the world's (granted the world in real life can go to fuck) is a horrible decision, but it had to be done.
4) Her death was also going to be completely painless. She was going to be put under anaesthetic, and they were gonna operate from there. So she wouldn't have had a clue that either she was dead or that she potentionally saved the world. If his daughter was actually still alive, do you think he wouldn't save her?
5) The only way Druckmann can say Joel was right, was for allowing them to make a sequel and constant remasters / ports. No cure = more games.