Drawing Free Body Diagrams

Can't you just assume a direction, and if the force comes out negative, it's in the opposite direction from what you assumed?

 

Hmm...try looking at this:

http://en.wikipedia.org/wiki/Overdetermined_system

 

You didn't actually write down a well-defined problem statement. What exactly is it that you're being asked to solve for?

 

The reason there is no force in the x-direction at F is because the joint is a roller, it resists no forces in the x-direction. A force in the x-direction on a roller would cause it to move.

The idea your professor is mentioning is that if the joint at F was not a roller and rather a pin or some other type of constraint which imposed more than one resistance on the system, the system would be over constrained or statically indeterminate. These types of problems are solvable only through some sort of continuity condition such as material property relations that go beyond just performing force analysis.