I somehow ended up with a trade route from a barbaric city. I feel it is worth mentioning that the romans who previously owned the city set up the route. Not a gamebreaking bug, but something to watch for.
Bearcoco three things: for your first problem, click the fleet menu at the top and then go to your production screens. Second, you get 2000 coolant from a location in the city. It is a one time reward and was not produced by you. Third, as far as I know, influence comes into play when you conquer the whole perseus arm.
I'm giving it a 4/5 because it delivers good gameplay, an interesting story, but what you say to the doctor is just rude, crude, and generally unnecessary.