How to test if PWM mode is working correcly?
There are my options:


The default way to do this is to use an oscilloscope. These can be quite expensive.
Use a logic analyzer if the voltage is logic/binary (0 and 3.3 or 5V). These are very cheap.
The easiest way to know if it works without the devices above, is to lower the speed drastically (using a divider in the software, like 1000 or more to get PWM widths of 100 ms to multiple seconds) and connect the PWM output with a resistor and a LED to GND. If the LED flashes faster, the PWM speed is high, otherwise low. By using a stopwatch you can roughly calculate the PWM speed (taking the divider into account) and after the test remove the divider.
If the PWM is controlled completely from your Arduino (probably not), you can use a software counter and print it out afterwards to see the speed.