Electronic – Industrial flash (LED?) for rolling shutter

The kind of CMOS camera modules you are asking about all have global shutters (electronic shutters, not focal plane shutters). You control them through their bus, typically some sort of serial bus like e.g. I2C.

You can find modules where you have control over both frame rate and shutter speed.

I very much doubt any camera module has a separate shutter pin. You need to implement the bus protocol anyway, or there would be no way for you to get the image data...

As @DeanB said, the assignment shows exactly how to do what you are asking. It seems you are just stuck on some sort of mental block, it happens to everyone!

For the low-pass circuit:

You are given the following schematic:

And an equation that describes its transfer function, then they even solved for the cutoff frequency for you. Which comes out to be as follows: $$ \omega_c = \frac{1}{\sqrt{R_1R_2C_1C_2}}$$ From here it is just some simple math to figure out what values you need for the low pass circuit elements.

For the peak detection circuit:

You are given the following basic circuit:

This circuit is a little bit less intuitive than the low pass filter and I can see how this could be a bit confusing. Conceptually, since you have already put your signal through a low pass filter, the peak detector is looking for quick rises in the input signal. These quick rises correspond to bass hits. If you have a bigger input signal, your output capacitor C1 will charge more fully and your light wil stay on longer.

Your design factor here is essentially just the decay time of the peak detection circuit. Which is determined by: $$\tau_{td} = R_1C_1$$ So if your $$\tau_{td}$$ is too small the light won't stay on very long, and if it is too big you will miss bass hits.

This is where the engineering comes in and it is up to you, as the circuit designer, to play around with the values and create a useable circuit. Best of luck, and let me know if you have any more questions.