Generally, you need a "license" when you need special permission -- like a license to practice law or medicine. There's usually no special "license" needed for graphic or web design. However, if you are doing your freelance work under a name other than your own -- for example, "Robin Smith Graphics" (instead of just "Robin Smith"), you will have to file a business certificate with the local county clerk.
Confirm with an attorney in your state to make sure you're following the rules properly.
The fall in new company starts does not necessarily mean that the American economy is less dynamic than it used to be, or that Americans are opening up new establishments at a lower rate than they did in the late 1970s.