Can you give me an example of something that players will do in asteroid bases specifically?

If you go to one of the encounter asteroid bases, you can find bodies. You can kill X amount of guys. That's more for the mission ones, but they will always be populated, so you don't need a mission to go there. You can just go there and check it out yourself. But these are more like the playground for missions. But you can also find other ones that are inhabited, and you can just explore and do puzzles in them. At least that's the plan going ahead.

And certain kinds of puzzles and treasures to be found.

Yes.