Duc
1:At the start of the race you will have a lot of fuel in the car so the lap times will be slow but at the end of the stints you will have less fuel so your cars will be lighter so you will have faster lap times.
2:You said that even pushing the lap times take so much to improve because when you are racing you also have to maintain the tire temperature because if the tires are too cold or hot it will like "lose" time to the cars with optimal temperature
I try to keep the temperature in the middle of the gauge as much as I can. In the first stint I can notice the performance discrepancy the most. It is quite weird as my drivers aways qualify well but then they lose a second or so per lap, even compared to cars with similar strategy :(