I've read the FAQ and the big thread on Diplomacy, but I want to clarify a few things.
First off, there is simply no way for a race to peacefully accede to your empire, right?
Currently, no. But some form of Amalgamation (in the Starfire sense) is on the list.
If you want more than one race in your empire, you have to conquer them.
Currently, yes.
Second, no matter how friendly you are with another race, you basically can't share a system with them, right? Even if they want completely different kinds of planets than you.
Wrong. If you are friendly enough they won't mind the presence of your ships in 'their' system.
Once you've got more than one race in your empire, how can you see the colony cost from the other race's point of view?
By choosing the other race from the race dropdown box (top right on the F9 screen).
Also, a question about the Galactic Map somewhat relevant to the subject. I'm not sure if this a bug or something I'm just not understanding. I'm in contact with two NPR's at the moment. When I click the box in the System Details sidebar marked "Control Empire", there's a choose box with all three empires in it.
If I select one of the alien empires, their flag shows up on Sol system, and nowhere else. While if I click on my own empire, my flag doesn't show up anywhere. This seems odd to me, but perhaps there's something I'm not getting. I would have thought that box meant, 'systems controlled by empire X'.
No, it means "mark the current system as controlled by empire X - merely for display purposes, and only for the currently- viewing empire, and not in any way that affects and computer function or game setting, but merely by displaying the appropriate flag on the current race's view of the galactic map."
It's a Post-It (tm) saying "Here be bad guys!"