Is there any evidence to suggest that there is an indivisible discrete unit of time? Perhaps matter and energy are continuous but time is what allows them to interact.

Hey, a few things. Energy and mass are not continous. Second time does not exist and is only an illusion that is a side effect of our being able to record our measurements. Lastly you might be interested on reading on the "indivisible unit of time" equal to 5.4x10-44 where any unit less is meaningless.

I do not know much about this, but as I understand space and time can be trade for each other depending of the gravity field the observer is located, or speed at witch the observer is traveling. So if time is and illusion would the same apply to space.

Also if the smaller distance measurable is that Plank distance, and speed of light is constant, then the plank time must be and absolute time.

I mean if energy, mass, space, are discrete, and the highest speed is finite, I think that time is not and illution, it advance in packets and it exist regarless of measurement or not.