Why is timer0 the fastest timer in the arduino?
Timers 1 and 2 are configured by the Arduino core library to run the so
called “phase correct PWM” mode. In this mode, the timers count
forward from 0 to 255, and then they count backwards to zero. Timer 0 is
configured by the same library in “fast PWM” mode, where it counts
from 0 to 255 and then overflows back to zero in a single timer cycle.

You can, if you want, configure timers 1 and 2 in fast PWM mode. For
doing this, you will have to access their I/O registers directly. C.f.
the datasheet of the relevant microcontroller for details.

A couple of links:


the datasheet of the
ATmega328P
microcontroller describes all the possible configurations of the
timers (sections 15, 16 and 18 for timer 0, 1 and 2, respectively)
the source code of the Arduino init()
function
to see how Arduino core configures them.