Suppose I am entitled to use a weapon for home defense in the state of Florida. If I visit a friend for say 1 week, would the Castle Doctrine apply if an uninvited intruder entered the house of my friend and threatened my life (or the life of my friend), even though it is not my normal place of dwelling? Specifically, I am asking if the Castle Doctrine applies ONLY to your main places of dwelling such as the persons car and house, or if it can extended to a friends house you are visiting (and sleeping at). The friends house is also in Florida.
Generally, yes. Castle doctrine generally applies to anyone who is not trespassing on the property, not just the property owner. So long as you have permission from the property owner to be there, you can invoke Castle Doctrine.
It should be noted that Castle Doctrine is not a law, but rather a legal theory of a narrow self-defense claim. In general, Self-Defense in the United States breaks down to "Duty to Flee" vs. "Stand Your Ground" with the latter being much more common in the U.S. while all 50 states have Castle Doctrine in a private space (three do not have it codified but rely on state laws). Castle Doctrine simply means you have a legal right to "stand your ground" on your own private property regardless of the state's "Duty to Flee" stance in public spaces.
Florida is a "Stand Your Ground" state for purposes of self-defense, which means that, so long as you have a legal right to be in a space, you have the right to use deadly force in self-defense even if you can retreat from the situation. And it's not something Floridians are shy about either. The concept of the "Stand your Ground" vs. "Duty to Retreat" entered into public debate a few years back during the Zimmerman case, where it was used successfully for Zimmerman to be found not guilty of murder of a teenage African American boy.
As a personal annecdote I like to tell, when I live in Florida, my boss walked into work the other day and was discussing his recent purchase of a gun and how, when asked by the police what the purpose of his gun purchase was, he answered to defend his home. The cop took him aside and said, "Just so you know, if you ever have to use that gun to defend your home, you need to know how to do it properly... Shoot to kill. It's less paperwork for us."