How can we know that the speed of light is constant? Science say that within a constant time frame the light travels a constant distance. But if time is relative how can it be possible to use it as a reference to say that something is constant?   
 A: You have this backwards. What you state, the fact that "time is relative", is a consequence of the theory rather than a cause.
Assume some light ray travels some distance in reference frame 1 and is seen also from reference frame 2. The trajectory is obviously different in both frames. That's nothing special that Einstein would have introduced : just try taking the bus and throw a ball vertically upwards while the bus is moving. You'd see the ball making a vertical trajectory up and down, but someone on the sidewalk watching it through a windows would see a trajectory which is a 2D parabola, not just a vertical line.
However, when this experiment is performed with light instead of a ball, the ASSUMPTION is that the speed of light remains the same in both frames (i.e. relative to all observers). THEREFORE, both observers see different trajectories (ie. different distances between "start" and "finish") but the SAME light followed both trajectories at the SAME SPEED.
The only way to solve the "same speed but different trajectories" paradox is to realize that a speed is distance on a time. Therefore, if delays and distances are relative to the observer, both observers could measure different times between two events. (The relativity of simultaneity would also take a part here, but you still see my point.)
A: Science does not say that the speed of light is constant.  Rather, a lot of people with fancy clocks and tape measures have expended a lot of effort measuring the speed of light and have discovered, to their initial surprise, that it is constant.  Then another bunch of people (largely one person) came up with a model - a bit of mathematics, otherwise known as a theory - in which the speed of light is constant as well, and that theory has, so far, matched experiments very well.
But it's the people with clocks and tape measures who count here: the speed of light is not constant because we are told it is by science: it appears to be constant because we measure it and always get the same value after correcting for errors and uncertainties.  And if, one day, we discover that we can measure it in some physical setup and get a different value, then we will have been wrong, and it was not constant after all and we would need new models. This seems unlikely to ever happen, of course, but what experiments tell us is what drives this, not the model: if the model differs from carefully-performed and repeatable experiments then it is wrong, and that is that.
A: We can't know that the speed of light is constant and this is why-
Say that the speed of light doubles between t1 and t2
Due to the universal law of conservation of energy the speed of every e.m. wave in the universe will double in that period.
What we saw as one second at t1 will now be perceived by us as 2s at t2 (i.e. there is twice as much going on so we will think it is twice as much time).
If we measure the speed of light at t2 (using our new perception of time) it will appear exactly the same as at t1, even though it has doubled.
So we can never be sure whether it is constant or not.
