Lets break this down to simple parts.
PA does not issue non-resident premits unless you have a permit from your home state.
Florida does issue out of state premits.
This link is for the FL CWP
Contact them and ask them if you as a New Jersey can get a CWP from FL and will it be honored in PA. From my quick perusal of the site i would say yes.
You ask good questions, but you need to contact the agency in Fl for the correct dope.
As to you your question of using your weapon you need to know what rules are for using your weapon. in general it requires a fear of loss of life or yourself or family. But YOU must know the rules that govern the use of weapons where you will be carrying. My best recommendation: Consult with a lawyer that is expert to firearms law and the use if deadly force for self protection.