It‘s easier for me to write in english and I think it‘s also better for the translator not to have it translated twice,
As mentioned in the mail from „TÜV“ for headlights it is sufficient to have the „E-Prüfzeichen“.
I think the TÜV is also right about the front bumper. Indeed the M3 uses the same parts, but M3 is a different car. It has a different type number and even a different manufacturer code than „normal“ BMWs. So „law wise“ it‘s a complete different car and things that are allowed on the M3 are not automatically allowed on any other F3x car.
Another argument from liontuning is that there is no imminent danger from mounting the M3 parts (or M3 styled parts) on the normal F3x. But the TÜV could argue that the front bumper has a huge impact on car aerodynamics and the whole aerodynamics on the M3 are different as well.
e.g if you want to mount the M Performance front splitter on your car, the papers say it is also mandatory to mount the M Performance rear spoiler - to keep the aerodynamic downforce balanced.
liontuning might be right that their TÜV had no problems with their project car, but every TÜV is different. I know super relaxed ones that say „as long as breaks and lights work - everything is fine“ and then there are others that adhere strict to every rule.
If you do the swap to the M3 front bumper and your TÜV is very strict and asking for a „Gutachten“ then you‘re in big trouble. And liontuning won‘t help you since they alread wrote that they can‘t help you and had no issues with their TÜV