Does Stewie kill anyone in this show?

Not all the time but he has killed people before like his babysitters boyfriend, matthew mcconehey, cleavland, supersotre usa manager, oliva and steve, and many others.

Well, let me think, he killed, I think it was Matthew McConaughey (shot an arrow through his head when he showed up at the door looking for Stewie because he had made his plane crash into the ocean). He killed that one guy that was the boyfriend of his baby sitter (he was jealous because he had a crush on the babysitter). He killed the kid who ultimately became Casper, the friendly ghost (though if I recall correctly that doesn't really count as he it was an accident(anyway that was in a flashback scene, so the veracity of those is more suspect than what happens in the regular scenes)). That's all I can think of for now.

Not in the shows i have seen, but he has dreamed of killing Lois.

None, as of yet. But Stewie has tried to, at least in 4-5 episodes, kill his mother in violent, yet funny, ways (like pushing her off the stairways).