No, you are not intended to do everything. In fact, in hard mode, you barely have enough threat to even get to the other side of the galaxy. You are just supposed to scout out what's to come and pick the lane you want based on the loot you'd prefer to get or the planets you think you can handle.

Kinetic is pure damage. The cold and warm both deal damage too, but not as much (until they catch on fire that is). Bio I believe just creates landmass rather than mining it. I never used it much, so I might be missing out on something, like trapping nests in rather than destroying them or something.

Safe travels.