“I’m on my way home.” (John Steinbeck, East of Eden) Is on my way an adverbial complement; home modifying on my way?

1. In the first example "the" is used because of generalizing. When you generalize about something (an object, an animal), you use the definite article before it if it is a singular countable noun. Some other examples would be: The horse is a mammal. The telephone is a useful invention. ...