1. No. Sport mode simply changes the shift points higher in the RPM range at 60%+ throttle. In theory if you drive lightly in sport mode you shouldn't notice any change in fuel economy even in stop and go driving.

2.Yes. I've been using 87 octane exclusively for 2 years now. The engine is designed to run on 87 although it will produce more power on 91 at full throttle. Some people have reported problems with 87 octane so you may want to get other people's opinion on this. Before you do try 87, make sure your intake air box is in the full cold air position all the time.

3. Fuel economy can vary a lot with summer vs winter gas, air temp driving style. 23.5 mpg is still execelent for this car. 27.5 is outstanding. I wouldn't worry about it.
As previously mentioned, the air flap should be in the full cold air position all the time. It is only an emissions device that is prone to catastrophic failure.

4. I can't comment on the fuel pump. I just replaced the fuel pressure regulator on our 240 at 120k miles. There is a simple test. After driving the car, remove the vacuum line going to the FPR and sniff for gasoline fumes. If you can smell gas, the FPR is leaking. With your excelent fuel economy I suspect it is not leaking but at 207k miles it might be a good idea to replace it just to be on the safe side. Another item that is over looked by a lot of drivers is the fuel filter. Might be time for a change. I know mine is.

Good luck.
Justin