Ok, i'v played a bit (just did the audition to become Rank E) and some things are clearer now, but i have some other questions now 
1) I did one of the special auditions (if i guessed correctly it's the one you need to do before level 13) and was pretty confused because i didn't get any stars in the first 2 sections only to find out that this audition doesn't have 3 sections but it's one single 27 appeal section. Are there more auditions that behave differently? Or is it just the special auditions?
2) There seems to be a timing for an appeal that is better than others. Is there an indicator which is the right timing or is the only guide to get that right my inner clock?
3) I have tons of accidents during a song (about 8 or so), is that normal? And what determines how often you can make an "appeal" or whatever it is during the stage performance?
4) You need to reach the next rank in a cetain time span. Is the time limit fixed on the week number? In other words: If i reach rank E earlier, do i have more time to reach rank D or is the time you have to reach the next rank always the same? Edit: Ok, i think Kotori just explained to me that the former is correct.
1) The special auditions are the only ones that behave differently. I believe "LONGTIME" and "HIT-TV" are the ones where it's a long 27-appeal section, if memory serves correct.
2) Usually I trust my gut on the timing of the appeals. Also, I believe the comments that the judges make throughout the audition make a difference in your appeal timing, since you're trying to get their attention. How often you appeal to a judge in succession also has an effect.
3) When you're early into the game (and therefore of a lower rank), it's pretty typical to have a lot of accidents during your performances. As you raise your stats and do better in auditions and rank higher, those mistakes should decrease. Mistakes can also occur due to a bad memory appeal or poor appeal timing.
4) I think the amount of time you get is always the same, but I could be wrong. Usually whenever I play, I don't go to the Idol Ultimate till the very last day so I can get my stats higher and do stylist appointments I may not have had time to do earlier or do more auditions so reaching the next rank will be easier since I'll need to gain less fans, but that's just my strategy.