PWM, PAM, PCM sine generation and usage confusion
Would I hear a sine tone or the speaker popping as if it was being
  pushed back and forth?


Usually, for audio, the PWM frequency is substantially above 20 kHz (and usually above 100 kHz) so the speaker (if directly connected to the PWM signal) would reconstruct the audio on the cone because it has mass and cannot move the cone at the PWM rate. In other words the speaker acts as a low pass filter. However, the PWM frequency may still produce cone movements that can annoy bats/animals but a human wouldn't hear this.

But, there will be energy lost in the speaker due to the raw signal being applied and this may not be negligible hence, an inductor/capacitor low pass filter is chosen that removes the PWM "carrier" content.

The same applies to a motor - a motor isn't usually as "agile" as a speaker and may be operated at a PWM frequency in the low kHz range but it can still present a problem with over-heating when connected to the "raw" PWM signal so extra low pass filtering is sometimes employed.


  Similar thing with PAM/PCM, if we have 50% duty cycle and PAM pulses in a
  sequence of a sine wave, what would the speaker output, a tone or a
  popping noise?


Again, the answer is similar; the "digital noise" is almost certainly at a much higher frequency than audio so some filtering may be required but it won't affect the sound quality or the sound produced if the PCM frequency is high enough.