rostfreyh: Can you just take these animals with you? Or can they be relocated to other planets, for example? Probably not. But maybe build a zoo?
They can be summoned on every planet and in the anomaly, but not in space stations and freighters.
And the companion you summoned follows you. The game seems to enables companions to "teleport" on the planet surface and in caves, if they are stuck or fall behind too far.
Riding your companion is another interesting way of transport. Not sure if all companions have the ability, but the one attached can jump quite fast and high and I can ride it up very steep mountains where walking and jumping was impossible and even the backback rockets were not sufficient.
Companions can hatch eggs but only on plant with compatible climate to their homme planet.