Oh-kay. That was fun a fun (and extended) lunch break:
First things first: Don’t install the "recommend" 3rd party YouTube app but the official one (with the ugly blue logo, but with youtube.com as manufacturer). It connects nicely to your YouTube account, and even without pairing the FireTV with specific devices, it acts like a ChromeCast: You you can push YouTube clips from your Android or iOS handhelds over to your FireTV.
Getting Netflix was a bit more of a challenge: While Netflix Germany finally launched about a week ago, the official Netflix App for FireTV is not yet available for (free) purchase – it’s still geo-locked. So I did as I always do: I switched my 1-Click® address and my Kindle country to USA (my “fake” US postal address is actually my PO Box at MyUS.com) – and without even bothering with VPN and whatnot, I could purchase the app, and it got installed on the FireTV.
The first launch of the Netflix app failed, I had to “Force Stop” it (I’m so glad that I’ve found the app list somewhere deep in the FireTV’s settings menu). Afterwards, it let me log on with my regular (US) Netflix credentials.
Best news last, but not least: Netflix Region Switching via Unblock_us works fine, it just requires a “Force Stop” of the Netflix app to make it refresh the country.
… Next stop: First side-loading Android apps (e.g. ES File Explorer to be able to stream MKVs from my NAS), then trying to connect other Bluetooth HIDs like mouse/keyboard combos … I’m also dreaming of using an OUYA controller. ;-)