How does deep sea life exist?

That is still unknown. In zoology, deep-sea gigantism, also known as abyssal gigantism, is the tendency for species of invertebrates and other deep-sea dwelling animals to display a larger size than their shallower-water relatives. Proposed explanations involve adaptation to scarcer food resources, greater pressure or colder temperature at depth.

They just live in an entirely different world than we would ever recognize. There are life forms which live in the miles-deep column of water who have never seen light - nor have they experienced the bottom. They're born and live at a certain depth. There's some who live on the very bottom - 5 miles deep! And they all seem happy enough.

Most creatures on this planet make their own light - they use it for camouflage or aggressive reasons. Living light is the most common form of communication on the planet. We don't make any, so we don't think much about it.

there's some very colorful books full of pictures of these deep-sea creatures.