How many bytes would I require to store few seconds of fan controller PWM signal?
The easiest answer is: find the maximum frequency in the signal, and double that. In the case of PWM, call $T_p$ the duration of the shortest pulse possible. The signal bandwidth is in theory infinite, but in practice, frequencies above $10T_p$ will contain very little energy. So, you can safely sample the signal at $20T_p$ samples per second.

If you need better fidelity, then sample faster, accordingly.

Now, a PWM signal typically has only two amplitudes, so you can use one bit per sample, or $20T_p$ bits per second.