[ QUOTE ]
Another thing to consider is that an aircraft to be used for flight instruction has to be insured as such, and many FBOs will only allow instruction in their aircraft to be given by their employees for insurance reasons.
[/ QUOTE ]The answer to this part of your question varies. In some parts of the country, CFIs are generally treated as employees of the flight school. But in others, CFIs are generally treated as independent contractors. Rephrasing your statement, in both cases, the insurance issue comes down to: most FBOs will only allow instruction in their aircraft to be given by CFIs who are approved by the FBO. It's also possible for an "employee model" FBO to allow some independents also. Whether it will or not depends on the FBO's general policies and whether the "independent" is bringing in new business or taking away business from the regular group of CFIs.
[ QUOTE ]
Is there insurance you can get for yourself as an instructor, or do you have to find a generous FBO, that has insurance that would cover you?
[/ QUOTE ]As others mentioned, yes there is CFI insurance. As far as FBO insurance "covering" CFIs, that usually means that the =FBO= is covered if the CFI does something wrong. That's not the same thing as the CFI being protected. =Never ever= assume that someone else's insurance protects you.