Transistors – Identifying Substance on Board

Those do not look broken. Generally electrolytic capacitors will have scored lines so that if they do break, the lines will pop due to internal pressure.

The orange bit does seem funky but I would probably write it off as some of that gunc used to hold the capacitors down.

When you drop to a low duty cycle, a motor will not be able to rotate due to the mechanical inertia. However, you are still pulsing the voltage onto the motor. So you are hearing the coils in the motor activate and deactivate rapidly but without enough energy to rotate the motor.

I usually put a lower limit on my PWM duty cycle in the software. I just turn the PWM off below that point.

As far as the scope issue. You may have had a static shock as it is pretty dry right now where I am. When it gets this way, I have to be careful to ground everything. Just touch the probe to a connector case, like one of those USB.

Or, you may have some sort of grounding issue that could cause a problem. Scope grounds are connected to earth ground, and that little metal ring near the tip is the ground, so if you are powered in a non-isolated way, you could easily accidentally short.

But since you specifically said the spark came from the tip of the scope, I would guess static is probably more likely.