but when you select a runway in the FMC, will it change your flight plan to send you to that runway?
If you mean the FMC. Yes it will. I often do the flight plan in the FMC and copy it to RTE 2 (before entering DEP, SID, ARR and STAR). That way, I can add the new information into RTE 2, activate it (but you have to make sure it goes to your next waypoint and doesn't try to return to the departure airport), fly the new STAR and TRANS.

Oh, and does that little circle icon on the picture of the plane in the Fuel and Payload window represent where your CG is?
Yes it does.

Mark