If I have a contractor license in Florida do I have to live in Florida to build there

No you don't have to live in Florida. What matters is that you are licensed in Florida and that you fulfill your duties on the project as the license holder.

Yes, but you still have to be able to adequately supervise the construction activities of the company. And if you're the primary qualifying agent then you're responsible for the financial status of the company as well. This will really come up if there's a problem on a job site and the DBPR investigates or a lawsuit is filed.