Can a timer be used in both CTC and (fast) PWM mode simultaneously?
Technically no. CTC and PWM are distinct modes of operation.

However, more advanced PWM modes, specifically mode 7 for 8-bit timers and modes 14 and 15 for 16-bit timers, allow specifying an arbitrary timer duration in OCRxA or ICRx while still allowing PWM operation using the other output compares.