Should you? Probably not. Are you required to? Maybe. It depends on the type of profession you’re in. Lawyers, for example, are required to be in professional corporations (“PC”). Forming as a PC may require additional restrictions in your bylaws, for example concerning ownership. So if you don’t need to, generally you shouldn’t. But you may not have a choice.
This is the person who signs and causes the filing of the Articles of Incorporation (or, in the case of an LLC the Articles of Organization) with the designated state authority. In a small business, this is usually the owner/shareholder/member. Some folks have their attorney sign the documents to help expedite the process, and that’s ok (but not necessary).
No, but thanks for asking a weird question. You’re likely getting confused with some industries, like talent management, that may require you to obtain a license from a particular state agency. The formation of the entity doesn’t trigger automatic licensure, nor does it automatically require you to get a license for your business. Licensure for your business is separate and apart from forming an entity. And, in some instances, if you are required to obtain a license, that may dictate the kind of entity your form.