this is all an opinion and in no way gospel.

a) I'm not completly convinced that chuushin/genin/jounin is a sound way of guaging fighting ability. If you'll recall, chuunin was mostly about leadership capability and fighting ability was rather secondary (otherwise shikamaru wouldn't have been the only one passed). It's my opinion that jounins TEND to be on a higher fighting level than genins simply because they've been ninjas longer.
b) As for sakura, it's a manga, does not deal in any way with real life or have to be controlled by how you think it should be written. We've all known that Kishimoto is going to do this for a long time and he certainly isn't too worried about what some american is thinking about the direction he's taking HIS manga in. I'm not saying that you can't express your dissatisfaction, I'm just saying the tsunade isn't a real a person and it's silly to do the whole freud thing on why she picked sakura. It was explained pretty easily in the manga and as far as storyline goes, it makes perfect sense.
c) Being someone's apprentice doesn't mean that you are their sole student. What it means is that you are their servant (for lack of a better word) and in exchange for your service you recieve special/extra training.