Regarding the question, it is true that the received pulse will be shorter or longer than the transmitted one (depending on whether the object is moving towards or away from the sensor) but since we are assuming that the speed of the object is significantly less than the speed of light, we're making the simplifying assumption that this difference is negligible. People sometimes refer to this as the "stop and hop" assumption since in practice we are assuming that the object "stops" at point x when the radio wave is emitted and then "hops" to x + dt*v once the wave has been received dt seconds later.
Regarding the number of cycles, you are again correct that the image represents a gross oversimplification. One reason for this is that since the carrier frequency is so much higher than the doppler frequency, the true graph of the received wave would not be noticeably different than the transmitted one. It is easier to plot a realistic graph of the demodulated wave which you can see in the plot titles "samples of the demodulated pulse".