For the offset compensation, Ccomp is integrating the current out of the gm amp. There's a clock and switches on the input and output of the amplifier that switch the polarity of BOTH the input and output, presumably with a 50% duty cycle.
Therefore, any offset in the amplifier increases the voltage on Ccomp during 1/2 clock cycle and decreases it during the other, averaging to zero.
The buck is a constant on-time converter where the on time is set based on Vin and Vout. At the start of each switching cycle the buck switch turns on for a fixed period of time. If the output voltage rises above the regulation point the switch stays off until it falls below the setpoint. Then the cycle repeats. This has the advantage that during transients the switching frequency can increase for very good transient response. In steady-state with fixed input voltage the switching frequency will be close to constant.