The receiver only needs its own batteries if it is being used in a nitro/petrol or the ESC does not have a built in BEC.

Power drain varies from radio to radio, some can chew them down quite quick while some will last for ages.

Some of the more modern radios are getting more power efficient, requiring less cells/voltage and usually lasting longer per charge also.

As you said though, 4 cells or 8 cells will drain at the same rate given a constant power draw, the difference is just the lower/higher voltage.