Yes, this likely qualifies as a form of stalking. How do you know these letters and postcards are from him? If there is an address you can trace it back to, you have something to work with.
You can't force someone to accept your apology. However, you may want to follow-up face-to-face to make sure the person knows that your apology was sincere. Pull him aside and...
This might not be the best reason to change schools. Consider telling your mom you have a boyfriend, so you can find other ways to spend more time with him.
Be polite, but firm. Explain to her that if she ever does this another time that your home is your space, or that you are busy and she isn't welcome...
The fact that you run into him every day may be a blessing in disguise, friend. It's great that you're willing to go "no contact," because that really helps you...
He may have distanced himself from you to avoid getting hurt again. If you're sure that you want to be with him, tell him! You never know until you try....