Actually I'm trying to figure out what is time and how it works, imagine there are only 2 photons in the universe (and assuming they are not traveling in parallel). Since photon do not have any inertial frame, so can I safely say that in this particular scenario time do not exist because otherwise the distance between the photon would change. Since time never exist there shouldn't be space let alone... never mind. My question is can there be a universe whereby there are only 2 photons in existence?
You are mixing up time and the flow of time. Spacetime is a four dimensional manifold, i.e. we need four coordinates to uniquely identify identify points in spacetime, and this is true whatever is occupying that spacetime. The fact only photons are present doesn't change the dimensionality of the spacetime (though it would make it conformal).
The trajectory of a photon is a 2D line embedded in the 4D spacetime and this line is given by the null geodesic equation. For any particular choice of coordinates it is possible to express the three spatial coordinates as a function of the time coordinate just as we do for moving objects in everyday life.
Time , tricky question. The rate that events happen? This would mean that time runs faster in the flame of a candle than it does outside the candle flame. However we evolved to quantify time by the seasons of earth. When to plant crops and when to harvest. For this reason our time is not the rate that events happen rather the rate the earth goes around the sun.
With this in place what if there were only 2 photons in the universe? I must object as I need to be there to make a few measurements. It is now 2 photons plus myself and test equipment. I will measure the speed of both photons. Unfortunately I and my test equipment are in the same space as the 2 photons so I will measure their speed to be c regardless of how fast time is ticking along relative to our crowded universe. Did not mean to weeny out but I see no way to measure the passage of time unless one is outside the system. The cause of the speed of the photons is proportionally effecting my test equipment so I will always say the speed of the 2 photons is c.