Can you study things in college that have nothing to do with your major, like just for fun?

Yes. You may register for any class for which you are eligible. Some classes have "prerequisites" which mean you must meet some condition before being allowed to register. Possible prerequisites include: that you are a sophomore/junior/senior; that you are a science major; that you have taken the previously numbered course; that you have permission of the instructor, etc.
Every degree plan allows for classes that are called "electives". That means you may choose any class you wish, within a given category. You may be required to take an art elective, or a humanities elective, or a diversity elective, for example.
Some electives will apply to your degree, but others may not. It depends on what you choose, and how many electives you choose in each category. Most people cannot afford to take classes that do not apply to their degree plan.

Yes, you can, but keep in mind extra credits cost extra! Take into account financial aid, and how many semesters (years) you want to be in school. I switched from a Graphic Design/Art teaching major to Social Work/Human Relations. :)

Yes. These classes will be part of your core/GE.

or you can just buy a text book on that subject