Why didn't Sirius escape?

[Mindy, a.k.a. CLH]

No: HPFGUIDX 24306

I'm sorry if this has been debated before, but I am wondering why Sirius
couldn't just transform back into a dog and disappear, once he was
captured. Why did he need the elaborate TimeTurner machination?

Also, I did kind of like Draco the first time I 'met' him in Diagon
Alley. I was kinda suprised that he turned out to be such a brat.

Thirdly, if Dumbledore is the greatest wizard of his generation, why is
he 'simply' a Headmaster of the School? Shouldn't he be the Minister of
Magic or an even higher position? Or is it THAT important for him to be
in the school because that is the training grounds for the next greatest
wizards of the next generation?