There are a lot of questions in your question.
Is life possible ?
We already know life is possible as micro organism in such a tight place.
I think it's possible for plants and insects.
In our environment, lichens and moss have no problem growing into very narrow spaces. Some leaf plants have very small roots growing between rocks, or between the cracks of the walls and roads. Once they reach the light, the leaves grow, and most of them are flat. If they have enough nutrients and enough light, they can grow.
You assume there is enough light, but I'm concerned with the ground and nutrients the plants will need. When the environment is too tight, earthly plants do not grow big. They can live, but they stay small. They are designed by evolution to find what they need in a 3D world and don't prosper when they don't have enough space.
For insects you can grow an ants colony in a flat design like that : .
I don't know whether ants are happy about it, thought. But they can live inside so, as long as your ants/insects are small enough, they can live and reproduce in your flat world.
Big plants and mammals ?
A big plant like a tree has big roots. I'm not sure whether a big tree could grow, but very tight and very long roots could bring a "big" plant the nutrients it needs. I'm not biologist, but I think a tree in your world could look like a big round surrounded by roots/branches with both leaves to gather energy from the light and roots to gather nutrients from the ground. As they die because there is no more nutrients, leaves and roots would decompose and become new nutrients for smaller plants (or even the "tree" itself), like in our world.
But I'm not sure for bigger animals. Mammals ? How could they find the place to reproduce, to give birth ? Either the animals are small enough to lay tiny eggs, or grow on themselves like corral, or duplicate like cells, but a very complex creature have complex organs that take a lot of space. Thus, deprived from the 3rd dimension, they should be very large to have the same organs. And they need energy and food, so now it's up to your imagination : are they going to eat plants ? To hunt ? How ? How could even eyes or ears work ? Or hands, tooths, all the ways to interact with environment ?
I think your question is very interesting but become to broad when coming to society. It's too different from our world, so here are a few thoughts but not a complete answer :
What do they need to live ?
If they are big enough to have a conscious, human-like brain, they will need space and living with each other will take space.
Moving a big organism seems difficult in this environment as plants have roots everywhere, you can't just step over it, you have to go through and break it, damaging your potential best source of food every time you step in "the woods". Living in community does not look like a good living strategy as this many "people" moving around will destroy the environment very fast.
How could they share information ? They can't draw, write... So either only communicate by touch/sound, thus their society could not evolve very much. Or they find a way (might be by sculpting edges of the flat-trees, like binary digits ?) to write something down. But it would not be as advanced as us with that.