So if you move toward a stationary sound source, yes, you encounter waves more frequently and the frequency of the received sound is higher. The wavelength decreases. No, the effects of shortened waves and stretched waves would cancel one another. There is no appreciable Doppler effect when motion of the sound source is at right angles to the listener. In this case, the source is neither approaching and crowding waves, nor receding and spreading waves.
Police use radar waves which are reflected from moving cars.
The Doppler shifts show that one side approaches while the other side recedes, evidence that the sun is spinning. The Doppler effect is about changes in frequency, not speed. The bow or shock wave is actually the superposition of many lesser amplitude waves that interfere constructively. When the crest of one wave overlaps the crest of another, and then another, a wave of greater amplitude is produced. A boat that makes a bow wave is traveling faster than the waves of water it generates.