Electrical – What PWM Frequency should be used for a 12V DC Gear motor

You should be fine. If a timer is being used for PWM it should also be useable to generate interrupts. Also, you should be able to use one timer for more than one PWM output. I mean, if they design the chip with 4 PWM outputs and 3 timers, there has to be a way to actually use all 4 PWM outputs.

What is the purpose of R2 in the first circuit? It's limiting the maximum current to the motor to 12V/220Ω = 54.5mA, which is probably not enough.

Just connect the motor directly to the collector of Q2.

You also need a couple of other changes: put a resistor (e.g., 4700Ω) between the MCU output and the base of Q1; otherwise, the B-E junction of Q1 looks pretty uch like a dead short to ground to the MCU. Similarly, you need a resistor (about 1200Ω) between the collector of Q1 and the base of Q2; without it, when Q1 switches on, it basically shorts the 12V supply to ground via the B-E junction of Q2. 1200Ω limits the base drive to Q2 to about 10mA, which should be plenty.