Is it preferable to pedal downhill? How do I use up less when I go down the hill? What is better? If I really drive down (I start down the hill fast and when I will at the foot of the hill I will have a rest since I slow down to my average velocity - in this point I will start pedaling again.) or if I have rest by the way down the hill and start pedal again at the foot?
(MTB rider here, XC &amp; DH, with little road exp.).

There is a certain speed for which up to that speed you should pedal, above it you gain more from adopting the most aerodynamic position and use gravity the best you can.

In my case I find this speed by trial and error in specific circumstances, because it changes according to slope, terrain, bike and tires used and length of the descent.

What I have found is that once you get to the highest gear and start approaching your max cadence, it is very difficult to provide the power needed to accelerate, and it may be even harder to do so while tucked in aero position. At this point, if the incline is steep enough, tucking in more will give you more advantage than pedalling.

In have one example, where a hardtail mtb with knobby tires on a paved road with little incline (I can ride it up at 20km/hr approx) this speed is around 42 km/hr. At this point I'm near max cadence in highest gear, so I adopt my aero position. It is common for me to even overtake other riders who are pedaling and when I get to the bottom of the hill, I can pedal harder because I have had a rest during the descent. In those descents, I get near 50 Km/hr just because of aerodynamics. (In a road bike in the same road, my threshold is near the same, and i know/feel my speed in aero position is much higher, unfortunately I don't have the numbers yet)

This works for me because in my general shape and level of fitness, on MTB rides, if I stop and rest for 3-5 minutes I resume pedalling approx 5 km/hr faster than if I pedal continuously. For longer rests my body starts to cool down and I have to re-warm up.

And this is where descent length comes into place. If the descent is long enough for you to cool down, (climate can have a role in this too) then the benefit of the rest you get, is negated because once you get to the bottom of the hill you have cooled off and will have to warm up again. For these cases, I recommend what some call "soft pedalling", that is pedal just to keep the blood flowing, sustaining the heart rate up. This can be done at intervals, alternating between aero position and soft pedalling, according to your cool-off time in that particular descent/climate.

You need to find a certain speed threshold, a simple computer will do. I know this is subjective, but there is a speed where you feel you need to put double the effort to get 1 Km/hr faster. In that point tuck in aero position an watch what happens with your speed.