First of all,
biology of a species that capable of surving in multiple environments
including changes in temperature, pressure and atmospheric content and
perhaps even radiation levels.
you're in luck because we already have that species here on Earth. Tardigrades are extremely tough animals that are known to have survived, among other things, the outer space - without air, and subject to direct radiation from the sun.
In your post you don't mention how 'advanced' you need your species to be. If they don't need to be a large land dwelling mammal equivalent, then you already have your answer. You don't need to explain anything.
If you need them to be a large land dwelling animal, then it is possible that it can bring in complications. All traits of animals are a result of evolution. And almost all traits are 'energy expensive', and often evolution tends to take the easiest path. Commercial strawberries, blueberries, etc are extremely rich in sugar, because of centuries of human cultivation. But wild berries have a much smaller sugar content, because sugar is expensive to produce, so it's only as sugary as it needs to be in order to attract pollinators in the wild. And those pollinators aren't as choosy as us humans, so they can afford to be less sugary.
The same principals apply here. You need to set up conditions which gives a species an edge over others when surviving such environments. Maybe your planet has a very volatile weather pattern where temperatures can wary from -20C to 50C (or even more) within days or even hours. Maybe that planet's sun is much more powerful than ours, and the radiations levels even at the sea level is much higher. You get the drift; set up the conditions in which being able to survive harsh conditions is a big evolutionary advantage.
The second part of your question, parasites, are an extremely complicated subject which even modern biologists have a minimal understanding compared to a lot of other fields.
simbiotic relationships where parasites in a creatures bloodstream,
lungs or dermis are directly responsible for coping with oscillations
in environmental extremes and excreting or repurposing inhaled or
absorbed material from the threatening environment?
again, we kind of have that in our world. Scientists suspect (not proven, but there's very strong evidence to support this hypothesis) that Mitochondria were once an independent life form, which at some point in our deep evolutionary history 'infected' Eukaryotas and started permanently living inside them, and turned out to be a symbiotic relationship, and now we can't survive without them, and they without us. You could argue that your second case too is not a far fetched one, but one that already exists.
How much detail do you want to go into? If you're writing a story you don't necessarily want to explain every single details of it, if you can base things in solid science, which in this case seems like you can, then that should be good enough?
I can recommend a few books about parasites for you if you would like to dig deeper. These are extremely entertaining books in their own right and can get you hooked even if you didn't need them for your research.