That is exactly what you'll have to hire a Florida attorney to appear in court in Florida to argue for you. Whether any of those things is true is what they will argue, and they will tell you whether it is better to fight jurisdiction and answer or fight jurisdiction and not answer, and whether or not you are correct based on the exact circumstances of the lawsuit.
Jurisdiction is a complicate issue that depends on FL's long-arm statue regarding what acts of an out-of-state defendant will make the defendant subject to FL's jurisdiction, and the details of acts you have done. For example, even you did not have stores or distributors in FL, have your product been sold into FL through the Internet and caused injury to FL resident? Does that injury make you subject to FL's long-arm statue? And, can you move the suit back to NJ court? To answer them, you need a FL attorney. And, since you have been sued in FL court, you will need a FL attorney to appear in the FL court to argue for you.
I concur with the recommendations of my distinguished colleagues. You need to retain a Florida attorney to fight these allegations. Most if not all states have Long Arm Statues, which allow s Court to exercise jurisdiction over a non-resident defendant. But, there are certain requirements that must be complied with in order to do that. Good luck.