I think that for helicopters it is one central factor that limits the speed of the helicopter, that is the forward moving tip of the rotor blade (The left blade tip if the helicopter rotor rotates clock wise) that can not move faster than the sound.
"Things" can move faster than sound, but then they will need to have a supersonic design. Subsonic and supersonic design is quite different. Often flight controls designed for subsonic flights will work in unexpected ways if they reach supersonic speed. I think I read somthing about Speedfire's during the second word that were able to reach the speed of sound when diving down from high altitude.
When it comes to fighter airplaines and supersonic passenger aircrafts I believe it is certainly not true that the jet engine can have a supersonic speed in the airflow into the engine.
I think all supersonic fighther airplanes use acombinition of first a supersonic "speed breaker" that will set up a shoch wave in front of the engine in such a way that the airspeed is braked down to approx transsonic speed before entering the air intake.
Supersonic aircrafts is easy recognized because of the design of the "supersonic speedbreaker" they use to have.
After the airspeed first is redused trough this "supersonic speedbraker" then the speed will be reduced further down due to the shape and geometry of the airduct/airintake. When the airstream enters the engine it has a speed well below the speed of sound, also when the aircraft is flying supersonic.
What limits the speed of an ordinary jetliner is also the speed of sound. They can not fly at the speed of sound but slightely under. Something like Mac 0.85-0.90 or arount that. The reason for that is the acceleration of the upper side of the wing to produce lift. Neither this can reach the speed of sound as this will make bad things to happen. (Wibrations, shocwaves, etc.)
I can't say for sure if the speed inside a jet engine is under the speed of sound, but I will believe so. One should remember that "the speed of sound" is not one exact value, but it is, as far as I remember a function of pressure and temperature. (Or was it only the temperature, I'm not sure.
The way an afterburner of an figher airplane work (or another supersonic aircraft) is that the temperature in the afterburner increases and the airspeed increases. Because of this the airspeed inside the afterburner will not reach the speed of sound before it reaches the final exhaust nozzels.
Some supersonic aircraft har variable geomertry that forms a supersonic shape at the exhaust nozzele while flying supersonic, but I believe some aircraft designed to fly at "slow" supersonic speeds has just a subsonic/transsonic exhaust nozzle. (Well most of them, I think has "a touch" of a supersonic disign.)
When you see the airintake, the ehaust nozzle, and the wings of an aircraft, It is normally rather easy to say approx which speed it is built for.
All this it because of the strange things that happen with aerodynamics at the speed of sound.
By the way, I believe most aircraft designers and pilots does not like the transsonic speed area, because everything is rater unstable. It is to fly subsonic to save fuel, and then to cross the limit of speed of sound as fast as possible to enter a more stable condition of supersonic flight.