Do I need a Florida based attorney to respond to a summons from the bank that is foreclosing on my late fathers home in Florida?

It depends whether you are named as a defendant in the lawsuit. If so, and if you want an attorney to represent you, they will have to be licensed in the state in which the lawsuit is filed. I would seek a consultation with an attorney and bring all of the documents, they will be able to advise what legal obligations, if any, you have personally.