A: Home Depot and other business owners can police their own premises as they see fit. Ever see the sign, "no shirt, no shoes, no service"?
It is their store and they can make the rules. If you enter a business premises with a video camera, without the business owners permission, they might not appreciate it for a number of reasons. Perhaps they are protecting their other customers who may not want to be video taped by some stranger (you). Again, it is Home Depot's right to refuse service to anyone and maintain their store as they choose. Home Depot would not allow you to come in and play the drums or practice your break dancing for the same reason they prohibit video taping. It is hardware store, not a movie set, and without their permission, you should not be in there doing anything that is not normal behavior for a customer of a hardware store.
A: No there is no such law. You are probably concerned with your privacy rights and whether or not you have agreed to be videotaped. In the case of a public place like Home Depot or Publix, you do not have a privacy expectation when you enter a public premises. As a general rule of thumb, an individual is not protected from surviellance in public places. Hope this helps.