Questions about Tap dial switch

No, the switch contains a battery.

Hello, the Hue app should have the latest software update. To set it up, press and hold the button with a dot or the first button of the Tap dail for at least 3 seconds. If this does not work, press and hold for 10 seconds. When the LED flashes between the keys, the search can be started under Accessories in the app. Be sure to wait at least 30 seconds, even if the tap dail has been found. After adding the tap dail, do not make any changes to the assignment for the time being. This is because a software update will certainly be necessary at first. Here is an example video:
https://youtu.be/uX0nyVN3vjc

Unfortunately, we currently have no information on the mini version.

Unfortunately, it is not possible to change the colour only the brightness

Switching is possible, I have also configured it this way. And a long press is then off again, in my case, for example. What doesn't work, however, is that you can only dim the last group, for example, when turning, but only one or virtually all selected groups at once.

Yes, that is possible

Yes, each button can be programmed to control a light individually, including colour cycling. The knob can be used to switch all the lights on or off.

Correct
Pressing button 1 switches the stored lamps on and you can dim them.
Pressing and holding button 1 switches the respective lamps off again.
Do the same with the other 3 buttons.