In the Agents of Marvel show they tell how the reason why Coulson survived was because he was injected or something with alien DNA and thus was "healed". He had his brain wiped because his body couldn't handle the residual effects or some shit (bla bla bla). As for Skye, I could totally see that. In the comics do the Inhuman's get their powers at birth? Puberty? Random?
In comics, Inhuman's are people experimented on by the Kree to perfect the Mutant gene implanted in humans by Celestials, and build a super army to fight the Skrulls.
Like Mutants, the mutations are latent. While a mutants x-gene/powers generally manifest around puberty. An Inhuman's manifest when exposed to the Terrigen Mists(kills everyone else). This is done in a ritual at "adulthood". A rite of passage.
Inhuman's traditionally were not like mutants, in being intermixed with humans. Where mutants are spontaneous in humanity. Inhuman's only come from direct offspring. They had their own cities, and society. A rigid caste system. with no upward or downward mobility. slaves stay slaves. When exposed to the mists, you are evaluated and placed into the proper caste. You might get powers, or you might turn into a limited intellect beast of burdern.
Eventually they moved to the moon.
recent push has retconed/changed things up a bit.
Inhuman's have escaped/left the society in secret over the years, and have had children with humans/mutants. so there ARE now inhumans intermixed with humanity. And, a revolutionary/terrorist stole terrigen mist, and set of terrigen bombs all around the world. Creating new Inhumans outside of the Inhuman society. Which lead to an attempt to "claim" them by the monarchy, as well as a the rebel group.