1) Does the gun have an intertwined-"S&W" logo on it?
Yes on the handle.
2) Do you load and unload the gun by pressing a latch on the side, which makes the cylinder swing out to the left?
3) If not, I assume that you load and unload the gun by squeezing two buttons on the top rear of the gun,
No buttons there is a lever on top, in front of the trigger, you lift up that makes the barrel hinge down and cylinder hinge up.
I assume that it is still considered a top break.
Does it have a visible hammer? yes
4) If so, does it have a trigger guard (loop of metal around the trigger), and does the hammer move backwards by itself when the trigger is pulled? These two features should normally coincide.
OK, my explanation of how to open a top-break wasn't very accurate, but anyways...
It's a .32 Double Action 3rd Model, manufactured 1882-1883.