FBO doesn't care as long students are signed off by a CFI(not their business anyway).
FBO keep the plane and make money by selling fuel and the owner rents the plane to the students.
You have to be sure that your students got proper insurance and the plane too.Check with owner.
yes, easier than in JARland as FAA flight instructor can teach without being attached to a flight school.
You won't make lot of money, but it' s a good start if you want teach a few hours a month. the only problem is with non US student as they need TSA clearance. I can not help you on this.