When using an external keyboard, how can use a function key as a function key (e.g. F10) instead of Mac custom control button (e.g. mute)? The built-in keyboard contains an
fn button, but I cannot find it in the external one.
The only way is to disable system-wide (that includes the notebook's keyboard) the custom control keys, and tell OS X that you just want to use it as normal F1-F12/F16 keys.
Go to System Preferences > Keyboard. Check the box that says "Use all F1, F2, etc. keys as standard function keys"
If you are using a Mac keyboard, there should be a Fn key. On the latest Mac wired slim aluminium keyboard, it is around the home, page up, page down area. On the wireless slim keyboard, it is to the bottom left.
You can do that with Karabiner-Elements:
It allows you to configure the Fn keys per device. In this case, I set it to use the default keys when on the external keyboard:
Also, you could try something like this utility.