It depends on where you conduct business. In California, for instance, we have a list of specific rules and qualifications for internships.
Rather than assume, I'd first Google 'unpaid interns' and your state name and then contact your state labor board to know for sure.
An internship is supposed to be a training position, so you don't have to pay.
However, if you're just using someone to do work for you and you aren't providing any real training, then I would say that you should ethically pay them. Not doing so is just abusing them and their situation.
Additionally, if you pay decently well, you will attract better interns. That alone makes it worthwhile paying them.
Yes, this is completely legal. Normally there are two types of internships in the US: paid or unpaid. A paid internship is (obviously) paid with the optional addition of a recommendation or school credit. Unpaid internships are also available as long as the employer can provide a recommendation which is convertible into school credit. Depending on the performance of an intern, unpaid internships may include a small stipend at the end for congratulations on a work well done.
I know you have selected an answer but an FYI some colleges require students to do an intern for credit hours towards their degree unpaid. Don't hesitate and call around to some colleges. You can, depending on the state, file it under your taxes.