[Questions] Some Android questions

If you really manage to install the firmware of an other device model, Google App Store will probably see it as a brick...

The only way to change firmware is to install "custom" firmware, that is third party. You can't (and shouldn't) install firmware from other models on your device because it will probably brick it. Custom firmware that supports your device is a possibility, but remember that the compatibility of the OS with your device will probably not change just because you install another device's firmware. Firmware handles the driver level instructions for devices, and if the architecture is at all different it could cause significant issues, assuming the device works at all.

Only install ROMs that is made (officially or not) for your hardware model (yes, same model code inclusive).
Otherwise, this will cause irreversible damage that totally induces desperation and rage.

check xda

I've tried to update per PC but all I saw on the screen was like downloading the firmware for few hours. I don't know if it was making it, but I've restarted it and I saw the old version. But it was not bricked.

BTW. One of my classmates has installed from an other phone on his S3. And it works.

Since you are so confused here is it simply put.

There is no official firmware available for the Tab 3, android 4.1.2 was the last update the device got - so you can't update it because there is nothing to update to. Your only option left is to load a custom ROM onto the device, but you have a high chance of bricking your device.

Your friend was able to update his S3 because it's latest firmware was android 4.3 while the Galaxy Tab 3's latest firmware is android 4.1.2