What happens when all passengers jump at once?
I will assume that the starting condition is level flight.


yes. momentarily the assumption of "rigid body" would not be satisfied. Also, for that 0.5s the aircraft would not be in contact with 10% of the weight, assuming constant thrust and velocity, you would have 10% more lift than weight, making the aircraft rise a bit before descend again when all the passengers land again. Velocity would not be greatly affected, as the drag would remain unchanged (no external change in shape or large attitude variations)
the difference between zero-fuel weight (ZFW) and Dry Operating weight (DOW) is probably what you are looking for. Airbus defines it as the "total traffic load". If you want to add catering, cabin equipment and the crew, you then take the difference between the ZFW and the Manufacturer's Empty Weight (MEW). As a percentage it can vary wildly based on the aircraft class (class 23 has much less cargo/passenger space that a class 25, for example)
yes. think of a beam in equilibrium on a pivot located at half its length: if you push just above the pivot, the beam will not rotate, any other location will cause it to rotate and flip over. This does not mean that the aircraft might flip over, as the beam is an uncontrolled and unstable system, while the aircraft is controlled, but it is a comparison that can help visualize the effect
I would define it more as shifting rather than jumping. This is a totally different scenario: the center of gravity at the end of this "jump" would be in a totally different location w.r.t. the start of the experiment, something that instead was not happening in the previous scenarios. By shifting the location of the center of gravity is likely that it might exceed the specified position limits and cause the airplane to be uncontrollable, to pitch up or down (depending if you shift the passengers backwards or forwards) and stall or nose-dive. On large aircrafts it is obviously not easy to achieve such unsafe scenario, as the cargo will be usually much heavier than the passengers, limiting the extent of the CG shift.