First off, he does die, 4 times as of episode 50. 5 If Yuuki killed him in their duel, though we have no way of knowing if they fought to the death, but I suspect they didn't. More importantly, Kirito loses most of his on screen 1v1 fights. If you don't believe me, I'd be happy to recount them for you individually.
The only time Kirito breaks the rules of the game is in his fight against Sugou, and that whole thing was a clusterfuck of rules breaking from erasing walls to spawning in legendary weapons.
The harem stuff is just kind of typical anime harem shit. Really though, it mostly makes sense with how it's presented, because like it or not Kirito is both incredibly strong and kind. Power is sexy and being nice doesn't hurt either. You also gotta consider, a lot of those girls that fell for him were in SAO. People were literally going insane in SAO. Most people were not in their right minds and it's absolutely no surprise that some of them latched onto anything they could. SAO was a combination prison and warzone and I would be shocked if the majority of SAO survivors didn't come away with PTSD, which kind of gets dealt with in the show with the special school they have to go to afterwards where they specifically mention that the teachers are watching them for signs of mental health issues. It's only natural for people to do crazy shit in high stress situations like that.
In short, I'm actually surprised more girls weren't throwing themselves at him. In ALO, he didn't really have a harem; just a sister with an incest fetish and 2 women trying to manipulate him. Sinnon pretty much hates him for most of Gungale. Yuuki doesn't really acknowledge his existence.