Yes the LEDs are under the computer's control. But that still doesn't make those LEDs "output devices" in the general sense of the word.
A modern keyboard is both an input and output device. At a high level its primary function is to input things into the computer; however, the USB HID communications are bi-directional communications, there is both Input and Output.
The computer can set the state of LEDs and some other features of the keyboard.
In some cases, the computer can upgrade the firmware on the Keyboard which definitely requires sending output.
Yes, but each of these functions have nothing to do with reading or viewing data, they are all about changing the properties of the device itself (i.e. firmware, indicators, etc.) If this was the definition then anything with a power indicator and power button would be considered an I/O device. But that's not how we define an Output device. An I/O device is all about data, which has nothing to do with the device state.