I recently read that there are more than 100 billion galaxies in the universe.
1. How and what method(s) do scientist use to calculate this figure?
2. How can a scientist state with confidence that there this amount when we cannot access other galaxies? Also how do scientist know where the universe ends and what if where we think it ends, it really does not end or what if the vast magnitude that we perceive is nothing but an illusion and it is not as large as we think it is
3. What really exists on these galaxies and how can we know?
Miramar / Pembroke Pines,Florida
The number of galaxies in the Universe is estimated from counts of galaxies in a small part of the sky, within the region we can more or less easily observe. Suppose that the region involved is believed to be one millionth of the overall size of the Universe and is observed to contain a hundred thousand galaxies; then if the number of galaxies per unit of space is roughly constant, the entire Universe would contain a hundred thousand million galaxies, or 100 billion overall.
Of course this assumes that we know how big the Universe is, and that galaxies are spread throughout it more or less uniformly. The latter assumption is probably a good one, because the uniformity of the Cosmic Microwave Background suggests that the overall density of various parts of the early Universe was about the same everywhere, and within the region we can study in some detail, any given part that is a few hundred million light years across looks (on the average) pretty much like any other part. There are undoubtedly regions that deviate from the average to a greater or lesser extent, but at least within the regions we can survey there is no evidence of large deviations over large volumes of space.
As far as the size of the Universe, we have no way of knowing how big it is, but when it is stated that the Universe contains so many galaxies we are not actually talking about the entire Universe, but only the part that is currently visible to us. The size of that region can be estimated with some confidence from the Hubble constant, which states how fast the space between the galaxies is expanding. If you go out far enough that the sum total of the rate of expansion of all the space between here and there equals the speed of light, then anything further than that is outside the visible Universe, and the distance involved is the "size" of the Universe. The distance involved is the speed of light, 300 thousand km/sec, divided by the Hubble constant, which is about 70 km/sec/Mpc. The ratio is about 4000 Mpc, or a little over 13 billion light years; so that is the "radius" of the spherical space centered on us that we call the (visible) Universe.
As far as "accessing" the other galaxies, we don't have to be able to get there to know that they exist. All we have to do is see them. And we can see them, at least as they were at some time in the past, throughout the distance between here and the "edge" of the visible Universe, providing there is nothing much in the way. In areas where gas and dust in our galaxy obscures our view, we can't do accurate counts; but there are regions where there is not much in the way and we can see "back to the beginning". It is in such regions that counts of galaxies are carried out. (I should point out that only the brightest galaxies are included in counts of very distant galaxies; but there are undoubtedly lots of smaller ones at such distances, just as there are near us.)
For very distant galaxies we can't know what is there, except in very general terms, because it is hard to even observe them; but for the nearby ones we can observe star-forming regions, clusters of stars, exceptionally bright individual stars and all the other things we observe in our own galaxy, the Milky Way Galaxy. Although there are minor differences in stars in different parts of a given galaxy, and similar differences between stars in different galaxies (primarily due to varying amounts of "heavy" atoms, compared to hydrogen and helium), we see the same sort of thing elsewhere as we do here, and in fact studies have been done of objects as far away as 7 or more billion light years that show that the laws of physics are the same in those objects as here, and that the atoms and molecules in those distant objects work exactly the same as similar atoms and molecules here. (This latter result is a very recent one, which was a great disappointment to cosmologists who had thought (or at least hoped) that the laws of physics might have changed over time, in which case the atoms and molecules in distant objects would be noticeably different from here. The best current evidence is that there is no difference at all, and galaxies here and elsewhere are pretty much the same.)
I think that covers everything you asked about, but if I have inadvertently left something out just let me know and I'll try to take care of the error.