I don't live in Florida, but I have a Florida LLC. I want to use the LLC to start an e-commerce site...?

YES! I do this with my business. But..... you'll have to run the business from Florida. If you work from home which is not in Florida, you're going to have tax problems. Fortunately for me, my business is a LLC in Georgia, and I live around Chicago, but my employees work from Georgia and I'm there about half the month. The other half I'm home, not working hard, or on the road. And I have a UPS Store mail box in Georgia.