Not visualizing signal in oscilloscope when a speaker is connected
Your drawing does not show a signal ground connection back to the Arduino?  Is there one?
Also, an 8 ohm speaker forms the shunt leg of an attenuator.  The series leg is the 100 ohm resistor plus the equivalent resistance of the digital pot.  The signal might be attenuated so much that it is below the quantizing level of the scope.  Can you increase the scope's vertical channel gain?
Starting with the signal level at the Arduino output pin, you can calculate the Thevenin equivalent voltage and impedance at the wiper of the digital pot.  This now is the signal source going into the 100 ohm resistor.  With Ohm's Law you can calculate the voltage across the 8 ohm speaker.
Note - the Thevenin equivalent values will change depending on the wiper position in the digital pot.  To see the full effect of this, run the calculations three times, with wiper positions of 10%, 50%, and 80%.