Spikey is right on both counts.
For #1, losing your home command station(s) is like losing your king in Chess -- that's it, you can't rebuild it. That goes for humans and the AI. However, the game doesn't end until all humans or all AIs have lost their homes. You can definitely retake the planet, but it's just like any other planet after that stage. In the 2.001 prereleases, in multiplayer games you get a home command station core in return for losing your home, which gives you a bunch of resources and such to help you battle back faster.
For #2, that is a known issue in 2.000, but is fixed in the 2.001 prereleases. The full version of 2.001 will be out in January with that fix in it.
Thanks for the report, and I'm glad you're enjoying the game!