You could have a couple different problems. For the fuel mileage issue, the flat O2 sensors could be causing the problem.
On a cold start, the engine is in open loop and is not using input from some of the sensors such as the O2 sensors. It is using pre-programmed settings plus temperature readings it is getting from the air sensor and the coolent sensor. So if the problem is a rich or lean mixture issue when cold, it could be the coolant temp sensor or the air sensor giving bad readings to start with. Another issue would be a leaky injector, sluggish fuel pump, or fuel pressure regulator. Also if you had a sticking idle air control motor it could cause the idle fluctuation. Not much you can do except throw parts at it but the best would be to get a diagnostic computer on it when cold to see what it is doing and to check the fuel pressure on start up.