I'll do my best to answer your questions but please realize that most of what you hear, here and elsewhere, is all anecdotal, it depends on the feelings and driving conditions of the author and is colored by the biased opinions of the author. I wish that Ford had a Forum for us with an engineer-type moderating who could give us exact answers in real time. I have suggested such a plan to Ford Marketing several times. I envision a Forum along the lines of the Dell Computer Forums, which I still find quite useful.
I have had my H-Escape for about 10 weeks and have almost 3500 miles on it. I have found that the Nav System Fuel Mileage display is at times most inaccurate, based on a comparison of gas-in and gas-out at the pump. I would say it overstates by 10%. It is still a good tool for trying to detemine patterns. I have found that you will not give the car long enough to build battery charge and properly warm up (in my environment of winter 30-50 degrees and hilly at high altitude) unless you drive it for more than a continuous 20 miles plus at a time. The longer I go the better the mileage.
1. Break In - I think the whole break in thing about mileage getting better with age is an old wives tale. I think mileage gets better because we drivers begin to hue to our cars and learn to drive them to the best mileage by watching patterns. That said I am seeing increasing mileage under the same conditions as the car gets older, and the EV time increases. I think this pattern would be the same in any car.
2. As I said, I have the Visteon Nav System so I seldom watch my dash gauge, and if fact, I think whoever thought up having the gauge showing how much electrical push is happening is a moron. Take out that thing and give me a digital percentage indicator of how much charge I have, or even a clock would be better. What I do always is take the number of miles displayed that is left before I run out (normally about 400 after a fill up), add another 60 miles because I think that number does not include the two gallons in the tank that is left when is tells me to fill up, and add both to the trip odometer reading. So if my starting figure is 460, I divide that by the 16 gallon tank and I am getting 28.75 MPG as I drive away from the pump. Most of the time I can maintain the total of 460 and sometimes more. When I quot my mileage to others I usually use my Nav figure instead of the lower figure I have just explained. That is my vanity I guess. I do not really watch the gas gauge dropping. Maybe someday someone will give us a gauge showing exactly how many gallons remain. I know NASA has been able to do this in their rocket tanks since the 1960's.
3. The H-Escape is not really a closed system because the driver has control over inputs. The way I have cycled over time and increased my battery cartoon from the original estimated 40%-75% to what I have now (low of estimated 15% and high of 90%) is as follows. To build the battery as high as possible I coast a lot and overuse my brakes. Not just using brakes, but heavy pedal pressure. To take the battery as low as possible I go on level back roads and parking lots and drive with almost no pedal to try to extend both EV time and distance. And when ICE comes back I try to get back into EV as soon as possible. It is almost like potty-training my car. But I think it has paid off. I am almost imagining that my computer firmware has an interactive side to it and is learning me. I don't know.
4. The EV will kick in sooner without a very very light foot and a low charge. I have also noticed that sometimes I expect something and something else happens. That seems to substantiate your 'algorithum vs. data' statement. I have hopes Ford will soon give us a good, less conservative firmware upgrade. I believe I am almost to the point where I can predict EV and force it on and know when ICE will kick in. At first I was able to stay in EV up to 30
MPH. Now I can stay up to 40 and get into EV at 40. Knowing the battery charge is important and I am glad I paid the extra King's Ransom for the Visteon Nav. Keep playing with your car as though you were back in HD Chemistry Lab.
5. I have heard of the dreaded "service emission system" alert on other forums. I have not seen it myself maybe because I pay so little attention to the dash display. It seems to be a transient condition, I would like to hear what your dealer finds. I would not be too worried.
Keep posting and I will keep giving you my best guesses.
Mike