Awesome! To the questions:
1. Yes on all that with the BP. Although in terms of affecting costs, your influence with them affects only the BP costs in politics, not anything else. And it doesn't always affect that, it depends on the race.
2. Yes, the minimap supports that, it was the third button up there next to the plus and minus. I should have shown that.
3. Battle clock is a good idea, I'll add that to the notes.
4. The cesium is mainly to gain some influence with another race who needs cesium; it's only good for those who don't already have an abundance of it. I doubt strongly we'll do a game encyclopedia, but the contextual information should spell everything out right when you need it. Right now it does some of the time, and not most of the time. That's one of the big reasons this is still Round 0, is because I'm still wading through all those contextual explanation needs.