Those pins are normal digital pins. The timer input and outputs connected to those pins are something extra. The Timers will only use the pins if that is programmed in the registers.
Even the A0...A5 are normal digital pins, The analog section is an extra.
The interrupt pins, the I2C bus, the SPI bus are all something extra for normal digital pins..
The pinmapping drawing is very useful. Google for : arduino pinmapping
Arduino uses TIMER0 for the timing. You should not change that. You can do whatever you want with TIMER1 and TIMER2. Some functions or libraries use those timers (pwm, tone(), and many more), so you have to be careful how they are used.
Yes, the Arduino timing and pwm can both use TIMER0, that is why the PWM for TIMER0 has a different frequency.
The pins are not gone for normal use (output or input pin), but they are gone for PWM.
Delta_G mentioned the software PWM. Such things are often used for Servo motors, frequency outputs, and so on. It uses a single timer with interrupt. Inside that interrupt the pins are set high and low. That way every pin can have a 'software' pwm.