Calculating the age of the universe Is the calculated age of the universe that of the visible universe or the entire universe? I dont know how the age is calculated but if it is believed that all we see visibly IS the entire universe then that means it is finite. If it is not finite then the light from the really far astronomcical objects has not reached us yet so there is a possibility it is infinite.
Can the method used to calculate the universe age since the Big Bang guarantee that it has an age or is it possible that it existed infinitely?
It is a common point of confusion, but an infinite universe can still have been at a unique singularity in space-time at a finite time in the past. 

This singularity is not a "point in space", since every point in the universe participated in the big-bang. It is merely a time at which the scale factor, which multiplies the separation between all spatial points in the universe,  was zero. 

So in cosmology governed by the Friedmann equation, the age of the universe thus calculated is the same whether you are talking about the "visible" universe or an infinite universe. The light travel time really doesn't come into this, because different parts of even a very large universe can be causally separated yet still have originated at the same singularity.