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School systems are subsidiaries of the state government. However, the school can do fund-raising to make extra money.
However, you're right that the schools can't open retail businesses. However, fund-raising is allowed.
Yes, a school district is a sovereign entity - a branch of the state government.
Fund raising is short-term while a business is a continuous operation. If you think the school is acting improperly, your best option is to contact the state board of education and report what they're doing. If it is illegal, the state board of education will stop it.