Hi Mads,
thank you very much for your reply and the informaiton you gave about the misteriuous question-mark-button!
Please don't try to update to the newest version. You will see no difference because you already completed the tutorial.
Two miles isn't bad at all!
What is a good distance to cover in one round?
If its too short, the user may get frustrated that he covers just a very short distance. If its too long, the user may become bored as his skills improve and he has to cover a long distance before it becomes challanging for him.
When I was designing the game the question of how long a game round should last appeared. I had no idea what the best value was so what I did was looking at other successful game titles. Some friends who never played Doodle Jump tried it on my device and I realized that during their first 10 rounds they stayed alive for about one minute. This is the value I tried to get close to.
There were already complains about the speed at which the car changes lanes. I increased the speed and the people who were complaining were satisfied. But then the complains came again, from people who didn't experienced the even slower version. I increased the speed again and this people were satisfied too. But then the complains came again, from people who …

It seems like the lane changes can't be fast enough. Of course it's easy to miss something that is 3 lanes away but this is the nature of the game. It's not just about skills but also a little luck.
May I ask how exactly you control the car? I play with the device in my palm and control the car only with my thumb with short swipes. I've got the suspicion, that users are playing with two hands and control the vehicle with the index finger. Maybe they don't swipe 3x in a quick sequence to change 3 lanes at once but change lane after lane. Another issue could be that they don't do it with short swipes but swipe all over the screen, which takes more time.
Just a suspicion I have to keep an eye on.
That's true, cars do really not move faster than you do if you honk. The reason is, that the horn signal serves another purpose. It just gives you the ability to get through if all lanes are occupied with cars in a single line. To avoid collisions there is the ability to brake though.
Do I get it right? You drive behind the gray trucks all the time? If so, just pass them.
That's a long post! I'll address each paragraph, in chronological order.
My problem is not necessarily with how long I stay in each game, as long as that is based on skill rather than luck. The distance covered doesn't matter, as long as one can increase it by getting better at the game.
This does not seem to be the case though. The formation of the other cars is something the player has no control over, but it makes me miss a lot of those power-supply-things. If and when I miss just a single one, there is a great chance that I will run out before reaching the next. It has occurred to me that it's difficult to stay alive, if you miss just one power-up. Then when you miss one (and it's because the car can't change lanes fast enough, or you're trying to pass a car), it's really frustrating.
I found that I can't stay in the game longer, just because I play more. Rather, I can sometimes stay longer if the batteries spawn in a place I can reach.
I play on a 10-inch tablet, holding it like I would a book. I'm using my thumb to swipe, and I do know that 3x-fast-swipe will make the car change lanes at once. It's solely the speed at which the car flows over the screen, that makes it difficult to grab anything, if you didn't reach right when it spawned.
I will admit that I don't brake very often. Are you assuming that people will brake when changing lanes, or did you go normal speed when you designed it?
With the grey trucks it get's even sillier, because in that zone you're trying to pass them all the time. Thus, it's impossible to get power-ups if they don't spawn in your lane.