Did Nemo escape?
It's never said. It's open to interpretation. I'd categorize it as an open ending movie.
An open ending is a film technique that leaves the audience in a state of ambiguity about the story’s ending. Open endings have no obvious meaning, but the ending can be interpreted in a way that is pleasing to you. In other words, watching an open ending is a matter of taste, and the ending can be whichever you like.
I like the analogy from Matt Neufeld - DC film Institute:
In many ways, we’re all continually trying to just survive. And, in a way, we’re all trapped, somehow, in one way or another. And while we may not be trapped in high-tech high-rises or on remote deserted islands or in remote farmhouses surrounded by creepy slow-moving flesh-eating zombies, we’re all trapped in life, in some way, whether we know it or not, whether we admit it or not.
And, as “Inside” so intelligently teaches us, all of us have to keep fighting to survive, no matter what stands in our way, and all of us, every day, have to keep trying to escape the worst of things to find our way back to the best of things. It’s that fight to survive that keeps us going, that keeps us sane, that keeps us alive. Because when we lose that fight to survive, we lose our will to live, we lose ourselves and our souls, and when that happens, the movie fades to black, the end credits roll and the story is over.
Now, Tom Moore also explores possible endings, but it's interpretation too:
The first is the most simple — Nemo escapes out of the skylight and either gets rescued or suffers the same fate as the pigeon did outside the window. The other is that maybe this ending is meant to represent his death and ascension to a higher power. Frankly, it seemed like Nemo was initially going up there just to put himself out of his misery, so a more tragic ending isn't too far-fetched. However, it's most likely that Nemo does escape since the panel crashes to the ground and Nemo would definitely take the opportunity to escape. While we don't actually see it, Nemo seemingly escapes this nightmare and leaves with new perspectives he couldn't have expected to gain walking in.