This is a Frame Challenge
An Earthlike zero-G environment has a problem: nothing sticks to the ground. The water, the dirt, the leaves and needles that fall off trees, dead creatures. Everything would be floating around inside the Ark. In fact, the slightest change in trajectory of the Ark would result in whole trees and boulders lifting from the inner surface of the Ark to float around in the void. And once the grasses and trees left a bed of soil (without regular water, no less), they're dead.
Water would break apart into droplets, rarely forming more than a cup or two in volume, especially as it's broken apart by the passage of more massive objects. Like dirt. Objects would move around and collide and, in my opinion, little life beyond molds and fungi would survive.
The only way to avoid this is gravity, whether created artificially with spin or using Clarkean Magic like gravity plates.
But, let's ignore that and answer the question
Things like flight and swimming rely on gravity. It's easiest to see when considering how a bird glides. The mass of the bird is pulling it toward the Earth. The outstretched wings, like a parachute, are pressing against the atmosphere. The atmosphere compresses, providing a "surface" that the wings can glide on. This is a long way of saying that birds when not flapping their wings are really falling with style.
Fish are a bit different because they use various means to create buoyancy. If a fish had the density of a rock and, for example, no air bladder to offset that density, it would sink to the proverbial ocean floor unless it had strength to swim upward at a constant acceleration to avoid falling.
You don't have gravity.
Once again, ignoring my frame challenge (not a small thing), fish in water would begin to stop using whatever mechanisms they once depended on for buoyancy. Air bladders, for example, would no longer be needed and would begin to atrophy. Without the force of gravity, the muscles needed just to swim are not needed to the same degree (although, ignoring my frame challenge, they'd still be pushing against the medium of water... it's really hard to ignore my frame challenge). So I can believe there would be some overall muscle atrophy as well. They'd be really soft eating.
Birds, I don't believe, would change all that much. Rather than gliding against gravity, they'd learn to glide against their own forward motion. They'd take a flap or two, not down, but forward... then they'd do nothing and simply blob along like a water balloon until they needed a course correction or to stop their forward motion, then they'd bring out those wings and do what they did before, just rotated 90 degrees.
Thousands of years isn't enough time to evolve anything (that would take millions and millions of years). But it is enough time to adapt, and adapt the creatures would do. I suspect most animals would become more playful in zero-G. Could you imagine what a squirrel would do in that environment? They'd have the time of their lives launching themselves across the Ark chasing one another. The wonder is that they'd learn (by rote of death if nothing else) to judge the force of their jumps to avoid splatting against the ground on the other side.