Could it be true that when the plane is falling to crash, one should start to jump. If the moment the plane crashes, you are in the air then, you are not affected by the momentum. That is very unlikely to happen. Is it true or what do you suggest to do?
Here is a video of a 747 taking off from Bagram Air Force Base in Afghanistan. Shortly after takeoff, the plane stalled and immediately crashed. As a warning for those who might be uncomfortable with the footage, there were no survivors. (Link)
On 2 June 2013, investigators from the Ministry of Transport and Civil Aviation of Afghanistan confirmed the load shift hypothesis; three armoured vehicles and two mine-sweeping vehicles came loose and rolled backwards onto the rear bulkhead, damaging the aircraft and pushing the center of gravity outside its rear limit. Consequently, the aircraft became uncontrollable, pitched up sharply and stalled, and crashed moments later.
In any case, if you watch the footage, it should be fairly clear that no amount of jumping would have saved anyone on board.
From a physical standpoint, even if we ignore the fact that the plane exploded when it hit the ground, jumping still wouldn't do any good. The Mythbusters did a nice segment on this, where they discussed the case of a free-falling elevator rather than a crashing plane, but the idea is the same.
It's important to note that not all plane crashes are so catastrophic; not too long ago, there was a famous incident where some birds flew into the engines of a passenger plane in New York, and the pilot was able to perform a heroic emergency landing on the Hudson river, resulting in no fatalities. In such a circumstance, you should do exactly what the on-board safety instructions tell you to do.
Assuming the brace position minimizes the chance that you'll be injured or killed by whiplash or by striking nearby seats, passengers, or other equipment.
If the plane crashes like the one in New York, then you should listen to the safety lecture before takeoff and follow the on-board safety instructions. If the plane crashes like the one in Afghanistan, then it doesn't really matter what you do.
No, jumping will have essentially no positive effects, only negative effects. No matter what, you are heading towards the ground at high velocity, and gravity will make sure you will always hit the ground - there's no way to avoid this by jumping. What jumping will do though is make sure you are not secured to any part of the aircraft so you will get rag-dolled by the crash - or possibly even ejected from the airplane itself. What you should do is read and pay attention to the safety instructions given to you when you board the aircraft. In the event of an imminent crash, tie yourself securely to your seat with your seat belt and brace for impact by assuming the correct position as indicated on the safety card. Of course, you might die either way, but I can't imagine your odds of survival would be positively effected by you standing up and jumping at the point of impact.