Can particles travel faster than speed of light? If so, would the concept of "time" still remain the same?

Are there particles with greater than zero rest mass (that can be accelerated to a speed = or > than that of a source of EMR)?

When we cannot physically measure the speed of light (speed in a vacuum), what exactly we mean by "time"?

What are we expected to understand from the concepts of "Time Dilation" (Time appears to run slower) and "Length Contraction" (Distance appears to get smaller) - as we move closer to the speed of light?

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