Is the net force conventionally shown in a free body diagram? Is it standard convention to display the net force vector on a free body diagram? Internet searches seem to give mixed results. 
 A: I'm not aware of any such convention.  You can always show the net force vector acting on a free body as long as it is clearly labeled as such, to avoid confusion with any other applied forces.
I personally wouldn't include a net force vector unless there was a good reason to, like to illustrate some accompanying discussion.
A: The method that I usually follow (it works perfect and is easy to understand and also to find errors if any):-


*

*Choose an observer (in most problems specially with pseudo forces) place your observer at a place which makes the motion of other bodies comparatively easier to consider. [PHYSICS is based on how you observe things]

*In case of FBD, make two axes of your own such that you don't have to consider much components. E.G. if you are working on an inclined plane then consider the incline as one of your axes. 

*Then apply necessary conditions and find net "force" in  the axis that is required. If it is in force equilibrium then sum of all forces (" net force") along X-axis and Y-axis (one defined by you) must be zero and likewise.


Try to come up with new methods that you are comfortable with... ATB! 
