By the way, I looked at the video links you posted, and the captions are not correct,
from what I know about aerodynamics and the FAA regulations.  First, it is VERY 
illegal to fly supersonic outside a designated airspace corridor, usually located 
above a safe altitude of 30,000 feet or over the ocean many miles off shore, and 
pilots would lose their licenses (especially in the military) and be grounded 
permanently for a stunt like that.  
 
Aerodynamically, what is really happening is that the aircraft is transonic, between 
0.9 and 1.0 Mach typically.  The cloud around the aircraft is a condensation cloud.  
If the aircraft flies at transonic speeds in high humidity, only one part of the 
aircraft will be supersonic or very close, and that's usually just behind the cockpit 
around the wing area, in the area of the aircraft planform that narrows down like an 
old-fashioned coke bottle (hence the term "coke bottle design").  The drastic drop in 
pressure around the aircraft causes the temperature to drop rapidly, and thus the high 
humidity in the warm air suddenly finds itself creating 100% humidity in that portion 
of the colder airflow, hence a cloud and therefore the strange cone formation.  
 
If the aircraft were actually supersonic, the edge of the cloud would form at its nose.  
As the pilot speeds up from transonic, the condensation cloud would continue to move 
forward from its wing position at 0.95 Mach until it reached the nose at 1.0 Mach.  
 
And, on top of everything else, there is a good chance that car windows, house windows, 
etc., would have been broken by the sonic booms, had one been created due to the 
overpressure by the passing double-shock front.  That would have resulted in several 
complaints and thus the final result of paragraph #1 above.  
 
In the second video, the pilot, who was obviously showing off, did not remember the 
golden rule about flying in the transonic range.  That is, the aircraft is VERY 
sensitive in that regime, with the flight controls responding more vigorously than 
usual.  In his exuberance, he likely was pulling up from his flyby with too much force 
on the control stick, and he over-G'd the aircraft.  In that case, the wings snapped 
or the fuselage broke in half, spilling fuel into a hot engine already in afterburner 
and operating at high thrust settings, and thus the explosion.  At least he'll never 
make that mistake again.

Take care,
Sandy Miarecki