Do Schools Violate The Minimum Wage?

Yes they do.

If paying a sub-minimum wage is bad, then isn't paying nothing even worse? Interns make nothing; aren't their employers therefore breaking the law?

So then, what to make of schools, where students are compelled to perform homework -- and thereby violating the spirit of zoning ordinances, union regulations, and often, child-labor laws?

This is worse than sub-minimum wage, and worse than zero-wage. This is a negative wage, where workers are paying to do work.

Now you can say: "But the school is not gaining from their work!"

And that implies that the purpose of a minimum wage is to punish employers for making money. If the employer does not benefit, it is called a "non-profit" or "government" or "school", and they can pay their employees nothing -- or even charge their employees. But if the employer benefits, then he is penalized be being forced to pay a "minimum wage".

The minimum wage = punishing the productive.