1. This is a piece of cloth or other material, which you wear over your face. (Is this one correct? Is 'other material' correct?)

2. If I catch some fish, I won't be hungry.

2-2. If I catch any fish, I won't be hungry. (Which one is correct, some or any? Are there any difference between them?)

3. If someone finds me, I won't die.
3-2. If anyone finds me, I won't die.
(Which one is correct, someone or anyone? Are both OK? What is the difference?)

John, I can't think of anything else other than "cloth" that one would wear over ones face.

Both #2's and 3's are correct There is really no difference in meaning.