I'm playing with the idea of an alien race that uses ammonia, not water, as a solvent and breathes hydrogen. This is mainly because I want it to combust when exposed to our atmosphere. However, I want to know if this is a believable concept, i.e. not a dumb idea.
Using ammonia as a solvent would work, though if you want it to be pure ammonia, you'll have to keep your aliens quite cold, as it boils at -33°C. Aqueous ammonia solutions would work, but that does not seem to be what you're after. Ammonia isn't as broadly useful a solvent as water, but it does allow for lots of interesting chemistry to occur, including things like relatively stable solutions of solvated electrons, which are quite unstable in aqueous systems. Lots of biological reactions will produce water, so an anhydrous alien will need a way to excrete the water just as we have a way to excrete ammonia. Maybe your alien could excrete crystals of glycerol or urinate an alcohol or something like that. In any case, ammonia is a much better choice than a hydrocarbon.
Breathing hydrogen is a bit more problematic. The purpose of breathing oxygen is that we can break C-H bonds and combine oxygen with both carbon and hydrogen atoms to release energy in the metabolism of organic molecules. Oxygen is highly reactive stuff; we just don't realize it because we've evolved to walk around at the bottom of an ocean of it. If we breathed hydrogen instead, it would be far less reactive. Hydrogen will readily react with lots of things, but it typically doesn't release huge amounts of energy in the process.
One idea might be to have your aliens run a biological version of the Sabatier process. The reaction is spontaneous at low temperatures, though it would never actually occur without catalysis at liquid ammonia temperatures. This would give them a means of producing some basic metabolic building blocks from materials that are common in the universe as well as provide a reason for them to breathe hydrogen in the first place.
Ammonia can work as a solvent in place of water or in addition to water. Hydrogen is also very reactive so it could be a useful energy source. Also if a planet somehow had high concentrations of Boron then Boron Nitride could be a substitute for Carbon as together they form the same bonds as Carbon and life based on Boron and Nitrogen might use ammonia as a solvent as at the temperatures of liquid ammonia that reactions between Boron and Nitrogen could be more controlled. In this case the planet might have an atmosphere of Diborane, Hydrogen, Nitrogen, and Ammonia vapor. In this case the equivalent of plant life might get energy by reacting diborane and ammonia to produce sugar analogues and hydrogen while the equivalent of animals might react hydrogen and sugar analogues to produce diborane and ammonia. In this case the gasses that the organisms would breath would explode when in contact with air. Also liquid water in high concentrations would be too hot and too acidic for this type of life and if this life touched life on Earth both would mutually poison each other.