First of all, yes we can. We have tons of experimental proof. Secondly, even if the earth is flat or whatever it must still exist inside some form of a universe.
Not really, though. Big numbers are a separate branch of mathematics. A googolplex, for instance is more than the number of atoms in the observable universe, but it's way smaller than grahams number.
What it counts is not exactly the point is more of a definition exercise of what the upper bound is of what we can imagine it put in words. Sometimes it has functionality, such as the largest Mersenne prime.