What country do you live in? Denmark
Is beer as a product in general (commercial/non commercial) taxed in your country? Yes, it is taxed on the priduction side using a volume and gravity based table:
and standard VAT on the consumer side.
Are you allowed to produce homebrew beer, that is tax free? Yes
Is there some amount limitation of homebrew beer that you are allowed to produce without paying taxes? No, as long as it remains for personal consumption
Is there any legal obligation considering for instance an obligation to fill a report or announcement as a homebrewer and send it to your legal authorities in order to be allowed to brew beer at home? No