1. My mom headed my teacher's way for an apology. 2. He should have gone her way when she asked for help. (Not really used in this context. It's better to say "come to her.") 3. How could you head my way now that the zombies are all over you? You are correct that "head one's way" means to go where someone is.

Other ways to say "heading your way": .. headed toward you .. headed in your direction Yes, basically it means, "They are heading to where you are." 001. My mom headed my teacher's way for apology. This sentence is confusing. It is important to say who is apologizing to whom. Thus, I would say, "My mom headed my teacher's way to apologize," or, "My mom headed my teacher's way for // to receive an apology." You need the article "an" for "apology". Examples: .. I owe you an apology. .. You owe me an apology. I think "headed your way" or "headed my way" are used more often than "headed [person]'s way" but it's still grammatically correct. In this example, since the mother was going directly to the teacher for a specific purpose, I would rather say, "My mom went to my teacher's office to apologize // to receive an apology." Or, "My mom approached my teacher to apologize // for an apology." 002. He should have gone her way when she had asked her help. As I mentioned it is used less frequently when it's not "headed your way // headed my way // headed our way // headed their way." I think instead of "come to her" it would be better to say "gone to her," though. "He should have gone to her when she asked for help." 003. Almost perfect, except it should end in a question mark.