Is it possible to "own" an doodle, or a melody, or a sketch? to what extent are laws about intellectual property and fair use able to be upheld justly?

Yes, it is indeed possible to own these three and you can apply for a copyright and people will not be able to reproduce and monetize their products with these art forms without your consent. Fair use laws could be upheld justly if the person using your art forms without your art forms was not exploiting them but generally criticizing them, making parodies, or using it for scholarly work.

That's true, it's a belief in one god