Is beer as a product in general (commercial/non commercial) taxed in your country? It is commercially.
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? There is no limit whatsoever.
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? There is not.
^ this is correct. It is illegal to sell alcoholic beverages without several licences and certificates from various agencies and local authority (tax, environment, food hygiene) but no restrictions on home brewing for personal use.
You might find this discussion about UK brewing legislation is of interest...