Apple Magic Keyboard 2 native function keys don't work
It turns out that my problem was rare because the circumstances of it were rare too. I solved my problem successfully by upgrading from El Capitan Beta to the Stable release 10.11.4. I did this by downloading the installer from the App Store application (can be found in the Purchases tab), and running it on my PC. After selecting the drive on which the current OS X was installed, I waited around 30 minutes for the installation to complete. It was completed and I didn't lose any of my data.

Once I logged back in, I clicked on the Bluetooth icon while holding alt and shift, clicked on Debug and Remove all devices. After that, I reconnected my keyboard and it worked fine.