So giving it a name such as function(evt) just helps to identify it in the code making it easier to read?
On IE events are a global object, whereas on most other web browsers the event info is passed to the first parameter of the function handler. So no, it's not inherited.
True. That's another usability enhancement that can be added to improve the menu. For the purpose it's not a problem at the moment but it could be something I add later on. I imagine the best way would be to add a class to each list item depending on whether they have any nested ul's? Then style that class by providing an arrow or such to indicate it contains sub content?
Something that I noticed though is that the user has no way to tell if a link will open a submenu, or if it will navigate to another page. You may want to consider how to clear up that confusion for users of the navigation.