It is normal. I think the school may have some the social programs to help the needy students & need the pay slip to prevent any abuse / underserving students.

Not sure this one, I furnished the school the document coz I don’t mind. You need to validate with the other if you intend to refuse.

I think if you want to decline, find a good way to decline it, such as by informing the school via letter that you are doing own business & do not have salary slip. Give the letter to your children , let them pass it to the school so that your children do not have to be subjected to unnecessary pressure whenever the teacher ask them for the document.