were there any experiments conducted to discover something faster than light?
Yes, but they do not travel fast than light
Speed of light
There are situations in which it may seem that matter, energy, or information travels at speeds greater than "c", but they do not. For example, as is discussed in the propagation of light in a medium section below, many wave velocities can exceed "c". For example, the phase velocity of X-rays through most glasses can routinely exceed "c", but phase velocity does not determine the velocity at which waves convey information.
who discovered the speed of light in a vacuum Witelo what is the numerical value of it? As a dimensional physical constant, the numerical value is different for different unit systems. how important is it in the field of physics? It is independent both of the motion of the wave source and of the inertial frame of reference of the observer.
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Speed of light [SEP] Faster-than-light observations and experiments
However, the only physical entities that are moving are the laser and its emitted light, which travels at the speed "c" from the laser to the various positions of the spot. Similarly, a shadow projected onto a distant object can be made to move faster than "c", after a delay in time. In neither case does any matter, energy, or information travel faster than light. The rate of change in the distance between two objects in a frame of reference with respect to which both are moving (their closing speed) may have a value in excess of "c". However, this does not represent the speed of any single object as measured in a single inertial frame.