I'm not sure I'll get everything right, but I can give some of these questions a try. I think, in general, it's better to stick with one specific question. You asked several.
and, while mass can't travel at the speed of light, light or no-mass particles can't travel slower than the speed of light, though light does slow down through a medium, but that's something else.
First off I am not a physics student. I am more of a science
enthusiast. The question pertains to time and the speed of light.
According to Einstein no mass can travel at the speed of light. Now is
that based on time or is time excluded from the equation?
Time can't be excluded cause you can't calculate speed without time. without time, speed is meaningless.
E=MC^2 doesn't include Time, but that's not all there is to special relativity, though it's the most famous equation.
With the understanding of warping the space time continuum, someone
standing outside the warp/shift would see it as traveling at the speed
of light or faster.
Warp ships don't exist and they might not be possible so this is a hard question to answer. A more scientific term is the Alcubierre drive which is a theoretical method where faster than light (FTL) travel might be possible, by warping space. So, if you saw such a ship fly past, it would appear to travel faster than light, but you could see light coming of the ship (though very briefly) and the light wouldn't be blue or red shifted like you'd expect with regular travel - (er, probably, I'm not an expert in Alcubierre physics).
Similarly in an Alcubierre drive ship, you'd experience normal time, while if you were in a close to the speed of light ship, you'd experience time slowing and the universe would appear to get flatter. But lets keep in mind that neither might be possible and certainly, both are enormously difficult.
that said. Who's to say the photon in a beam of light is not in its
own space time shift. Where to it, it is traveling at a normal speed.
But we see it as the speed of light. As an ant sees us moving very
slowly... We see the moving fast. Size, distance, gravity, and time
itself are all factors, are they not?
I'm sure, from light's point of view, assuming there is such a thing, traveling at the speed of light would seem normal and traveling slower than that, impossible.
I'm not sure what you mean by distance, gravity and time are factors. Traveling at the speed of light, distance becomes squashed into nothing and time doesn't make much sense. Gravity is experienced as curves in space, which might not be what gravity actually is, but that's how it behaves.
Not sure that helps.