For example, I start downloading system update file and hit the power button to dim my screen.
What happens to CPU? Does it lowers its frequency or change its governor to powersave? Or does CPU frequency stay the same when I had screen on?
Basically, downloading takes little CPU.
I assume the reason you're asking this is because "Why does downloading eat my battery so hard?"
If that is the case, then think of your Cell (3G, 4G, etc) and WiFi as giant flashlights that you can't see (technically, sort of what a transmitter is). Network connections at high speed need:
There are free apps in Google Play like Trepn Profiler that show you exactly what happens to the CPU frequencies of all cores during a file download. This data is captured in the background so the screen can be off. They also show the CPU load and actual power consumption in mA or mW.
I've found that downloading a large file over WiFi uses more power than you would expect. Downloading a 100MB file over WiFi with the screen off consumed an average of 997mW on my phone. The idle power of the same phone with the screen off was only 27.8mW. That's a huge difference.
This test was done on a Samsung Galaxy Note 3 using a Monsoon Power Monitor. Airplane mode on. All unused apps and services closed.
Disclosure: I’m part of the team who produced Trepn Profiler.
It depends. It might act the same like when the screen is off, or it could be on a lower frequency. It is up to the kernel.
There are tools which gives you the control, how the CPU frequency will change when the screen is on/off like Device Control (need root).