If I rent a car & have full coverage, will I also have to buy Panama insurance too ??
You mean if you have your own insurance will you have to pay Panama insurance too?
My answer is most likely you will. Almost all car rental companies here will charge a mandatory basic insurance charge which they use to supplement their profit. They will quote you a low rate for the rental and add the insurance charge. You can still get pretty decent weekly rates including the insurance and it will let you sleep better if you scratch the car!
Have a nice vacation in Panama!