Absolutely, because you need to make sure that your food preparation equipment and methods are compliant with the legal requirements, so that you don't have any problems if someone tries to claim that you have breached the law. It is also to ensure that everyone conforms to the same laws and standards.
Probably. Call the city offices of the town in which you plan to sell your sandwiches and ask them. If you plan on being a street vendor in a major city, you will most assuredly have to be licensed.