What are the risks involved when doing a classic zero-g maneuver?
The biggest risk is improper execution.  If you build up too much airspeed and pull out of the dive at 4-G and break something, that will be your primary issue.

Your secondary risks will be associated with the fuel and oil system starvation if they depend on gravity for operation.  This risk is balanced by how long you can sustain 0-g flight.  Oil issues are bigger risk than fuel, as even if you did sustain 0-g long enough to starve the engine, you should get it back as soon as you are in positive G.  This particular risk will vary by airplane and I probably can't say something as general as "not typically a problem for short duration 0-g excursions".

An additional secondary risk is unsecured objects in the cockpit.  This presents a number of possible complications:


floating objects may distract you from aviating
floating objects may break something (the example of a window in the cockpit would cause a major distraction for the remainder of flight)
Most importantly, this can change your CG which can have dire consequences if something heavy enough gets moved far enough.


I wouldn't put risk of stall too high on the list, because you should be doing this with enough altitude and in coordinated flight so a stall would just be a simple recovery.  

As for whether this is an aerobatic maneuver, it is a lot like a departure stall but a botched recovery (pushing over to 0-g before the stall breaks) and only a passenger could say for sure what you were actually doing.

That leads into the last risk I can think of, and that is when your passenger deposits his/her lunch all over the airplane.  In 0-g that could get on the windscreen and obscure your vision.  Be careful!