Correct keyboard layout (QWERTZ) with Logitech K400 attached to an Android HDMI stick

I've bought an HDMI stick with Android 4.4.2 to connect a TV to the local network (stream, DLNA) and the internet (Video portals etc.). The stick comes with no input device whatsoever. So I decided for a wireless Logitech K400r keyboard. Unfortunately the keyboard layout used by Android seems to be American (QWERTY) although the language and location settings are set to German. So I neither get Umlauts nor special signs correct nor do the media keys of the K400 work. But there is an easy way to make all this work. I've recently seen some people suggesting to install an app called External Keyboard Helper to fix things, which comes in a demo and a pro version, the latter with costs. Fortunately I didn't need any of these for the Logitech keyboard plus I got all media keys of this keyboard to work in just three steps without any cost :)

Step 1

First I went to the Google Play Store and installed the Logitech Keyboard Plus app by Logitech Europe S.A. (See? No external stuff and without costs. Ignore anything that's written in its description about Bluetooth.)

Step 2

Then I opened the settings section and went for Settings > Language and Input (Einstellungen > Sprache und Eingabe). Under KEYBOARD & INPUT METHOD (TASTATUR & EINGABEMETHODEN) I activated the entry called Logitech keyboard (Logitech Tastatur) as shown below.

Step 3

Now a click on the field above that is called Default (Standard) and (here) defaults to Deutsch - Android-Tastatur (AOSP) ...

... opened a popup called Choose input method and there I've chosen Logitech keyboard (Logitech Tastatur) as shown below and confirmed it.

The default now is the Logitech keyboard:

Finally ...

... it's done. The keyboard now behaves as expected and also the media/function keys do work. It is however not possible to adjust or configure anything, because this presumes a confirmed Bluetooth pairing between the keyboard and the android device and the K400 is not a Bluetooth device. It would probably be a good idea for Logitech to make this app usable for all available Logitech keyboards, even USB and Unifying(TM) ones. Update: As of now it is possible to cancel the Bluetooth pairing attempt without leaving the application. So this app in fact can be used for USB and Unifying(TM)-based Logitech keyboards.