Strange circuit design for driving a fan with PWM
Low-side switching is easier to deal with using ordinary logic levels. High-side equivalents need a level shifter, be they FETs or BJTs.

R2 is a pull-down to set the default state to ‘off’ when the MCU starts up but hasn’t yet configured the pin.

No idea. Seems like it won’t work. If the cap were connected across Q1 collector / emitter that would work. I’ve used this technique many times, it reduces switching noise kicked back into the power supply.