Legal Question in Business Law in California

Whether you could run a home-based business on a military base is not a question of California law. It's a question of military law and of the policies at your particular base. Your best bet may be to ask the commandant's office. Alternatively, you can repost the question under military law.

I'm not an expert on California's business licensing requirements. Hopefully one of my colleagues with better information about such things will post another response. Whether you will need a business license after you move to another state depends upon the laws of that state. If you have some idea where you might end up, you may want to post your question again under that state.

Whether you will need a business license may depend upon the type of business entity you set up. Different rules might apply to, say, a sole proprietorship under your name vs. a corporation with a name of its own. Even if California doesn't care about such distinctions, other states might. If you have some idea what state you might move to, you may want to structure your business based upon its laws now in order to minimize your problems once you move.