Here is a in-game video of David Greco, the Italian current leader. Try to compare this lap with your (put them side by side) and you will see that he jump on brakes late, accelerate as soon as possible, get a perfect line all the time. Those guys are talented, not cheaters!
This is not even his best lap, but a lap he did just to show the steering ratio he is using (exactly the same of Alonso's). He got a wonderful 56.8xx
Think that he can do a lap like this even with fraps capturing the video (so it will slow down his pc).
David Greco (Ferrari Virtual Academy)
Fernando Alonso (real)
About the "fuel mistery", everything is pretty simple: whenever you manage to complete a valid lap, your fuel and tires will be restored (so new tires and 10 liters of fuel).
Other people already said that might be an advantage to start from 10 liters, having 5-6 invalid laps to burn the fuel and being lighter and then attempt their best lap.
There are 2 main problems with this also:
1)doing a single lap after 5-6 invalid lap could be really boring, but even requires a lot of concentration. If you can do it, good on you!
2)tires wear out just as in real life. As you will see in the real F1 during qualify, no one does more than 2-4 laps with the same tires. Although you will have less fuel, therefore less weight, worn out tires will influence your performance more.
By the way, don't worry you are not the only one at +4'' from those aliens! I'm fighting to get under the minute as well. I always do some small mistakes and loose a lot of time. My goal is to reach 59'', for now. I will keep practicing, and I'm sure time will get down, sooner or later!