Is hydrogen the same everywhere? Silly thought. Feel free to shoot it down 
Does a hydrogen atom undergo any kind of change subject to it's environment? 
If one were to study a hydrogen atom on the surface of Mercury, another above Earth, and a third in interstellar space - would they exhibit any difference/s?
 A: It is the same everywhere. 
The same holds for all atoms with fixed number of protons and neutrons. Helium was even discovered (through its spectrum) in the sun before it was discovered on earth. 
A: Hydrogen in the atmosphere of distance stars is the same as hydrogen in the atmosphere of our sun is the same as hydrogen on Earth is the same as hydrogen in deep space.
We know because we have studied the spectra of them all.
A: This is quite far from a silly thought although this is not apparent at first sight. Apart from a couple of details which are well understood and have firm physics behind them - such as the fact that deuterium and tritium exist in some proportion and the hyperfine-structure distinction between ortho- and parahydrogen, as far as we can tell all hydrogen atoms are exactly the same. This is in fact the case for all atoms and molecules: all iron atoms are exactly replaceable (so long as you take the right isotope) and nitrogen molecules are all the same (so long as you take them in the correct electronic, nuclear and spin states), and so on.
This is one of the most profound symmetries in nature and it holds irrespective of geographical / astronomical position, chemical history, temperature, and so on. How can we tell? Well, the very fact that we can do chemistry with atoms is why - the basic tenet is that the world is made of a finite set of "blocks" and that combinations of them make the interesting materials around us. The success of chemistry as a discipline means that there's something to that basic tenet.
How can we tell that atoms in places we haven't been are the same as here? Of course, our evidence for that is not as strong, but it's built on the fact that astrophysics works just using physics of different kinds we can see experimentally here on Earth. We can do spectral analysis of the solar corona, for example, and if we see energy levels slightly displaced then we can explain that as Doppler shifts or magnetic fields that let us explore a richer and (as far as we can tell) fully consistent physical picture. We can do chemistry on the atmospheres of other planets and, though it's rather hard, come up with consistent chemical explanations for all our observations. We can link the nuclear physics we observe in accelerators and reactors to explain our observations of our Sun and other stars and see that they match what we do here.
This represents another of nature's deepest symmetries that is (again, as far as we can tell) completely exact: physics is all the same wherever and whenever you do it. Emission and absorption of light works exactly the same as here, and so on and so forth. 
So what happens when something comes up that's not quite right? well, so far we've always been able to explain that as a result of new physics. Some of these observations are in play right now. For example, the physics of EM emission and absorption is (possibly) slightly different in other galaxies; to explain this a "drift" of the relevant constant (the fine-structure constant $\alpha$) has been proposed, and there are currently Earth-bound experiments to measure this drift going on. (also this paper.) So far, however, and despite the number of open problems in physics, no definite evidence for physics being different elsewhere has come up.
