In the comics, Hercules doesn't kill Thor. Their encounters are often part of complex storylines with various twists and turns, but not resulting in such a fatal outcome.
Sure. Thor and Hercules have clashed multiple times in different comic series. Their fights often stem from differences in power, ideology, or the circumstances of the story.
The Disney story of Hercules has some basis in the real myth. The core idea of Hercules being a heroic figure with extraordinary strength is there. But Disney simplified and modified a great deal. In the real myth, Hercules had to complete the Twelve Labors which were often quite dark and difficult. Disney took that concept and made it into a more upbeat and less gory adventure for kids. Also, the way Hercules' character is developed in Disney is different from the more complex and often flawed character in the original myth.