The speed of light squared is only a big number in the units you normally use to measure speed. The speed of light is 1 in units of the speed of light. Just like the length of a year is a large number if expressed in seconds, but not a large number when expressed in years. And it could be a small number when expressed in millenia or geological eons.

I will leave it as an exercise for the reader to determine one furlong per fortnight in terms of miles per hour or cm per second. And while you're about it, what is one mile per gallon in units of inverse acres?

As far as the speed of light being a constant, it wasn't until 1905, when Einstein proposed a theory in which the speed of light was a constant. Since the theory has been experimentally verified, it is taken as an absolute, but in Science, that will only be an absolute until a new theory comes along that explains things that Einstein's theory can't.

In Science, theories are only good until Experiments disprove them.

Actually, this relates to Einstein's theory of relativity, which as it happens has been proven experimentally to something like seventeen decimal points of precision.

As speed increases, time slows down (remember, "speed of light" - 300K Kilometers per second, so the time component is fundamental to it) - and in fact that has been proven by placing one atomic clock in a jet plane with a twin clock staying on the ground, flying the plane around the globe at high speed, and comparing the times on the clocks - the one in the plane ends up being fractions of a second behind the twin. Thus the theory that if one could fly at the speed of light, this "time dilation" would be such that an astronaut in a ship flying to Andromeda, which is 4 million light years distant, would only age something like 40 years while that 4 million years would pass here.

That said, there yet might be something that travels, literally, instantaneously - and that is the connection between what are called "entangled particles" in quantum physics. This too has been experimentally proven; in essence, when two subatomic particles (say, electrons) go their separate ways and a quantum measurement (like spin) that is unknown until the measure is taken, if the local electron is measured and found to have a spin of +1 then at that instant the entangled particle will also collapse into the appropriate spin (I think -1 in that case, but not sure). That happens instantly, even if they are separated by any number of light years. THis is what Einstein referred to as "spooky action at a distance".

At least, that's the best way I can describe this stuff