No, Naruto has not killed anyone. Although, he landed devastating blows to his opponents like Haku and Kakuzu, he wasn't the one who finished them off. Kakashi did both times.
Erza, however, was not killed in the explosion because Natsu had managed to save her and himself from death. However, it was likely Jellal the one that pulled Erza out of the Ethernano and prevented the tower from exploding.
Manga & Anime Differences The anime opens with Erza's death, but the manga chapter begins with her at Porlyusica's house to get her eye healed. When Erza comes back from her death in the manga, she dissolves away, however in the anime, a hand reaches out to her from a bright light.