and on the matter of killing his children, he didn't know they were his children until after they were dead. all he saw them as was people hired to kill him, so he killed them before they could kill him. when he found out about them being his kids he was clearly distraught. Which is why he threw himself off the mountain, punishing himself for what he himself did.
Honestly with how far away from who Cyclops was when Jean was alive, if she saw who he was today, and how similar he is to Magneto, i could see her being frightened. Wolverine hasn't really changed character wise, he's still the man she knew, he still will do ANYTHING to get the job done, which he always did.