I've a gaming mouse that works great. Nevertheless, the scroll wheel got broken last week. When I scroll down or up, it won't recognize all the movements, sometimes it will go down while I was scrolling up, and it's all crazy, it's impossible to control.

I'm 99% sure the scroll wheel is broken somehow, so I want to clarify that it's not my computer, USB port, drivers or whatever. It's the mouse.

So... can I desolder the borken componets of the scrolling wheel and solder new ones bought in internet?
Can I use different brands?

Here are some generic pictures. I think I should desolder the two components that are on the left and on the right of the wheel and replace them by new ones. The problem is that I don't know if the IC will recognize the new components, where to buy them, if the mouse will recognize all the movements, etc...

 

Yes you can. I hope you realize that you might break something. Check the simpler fixes first:

If the scroll sensor is optical, then simply cleaning the wheel and the optics would probably clear the problem up. There is a tiny outside chance that the light output of LEDs decreased over time making sensing of rotation of the wheel intermittent.

If the scroll sensor is a set of mechanical contacts then most likely the sensor is mechanically worn. Cleaning with a contact cleaner (observe ventilation precautions) might restore operation. Eventually the sensor would have to be replaced if you can find one for that particular mouse.