Hi Ania Marysia. Thank you for your interesting question. As you have already found out, the Polish language is full of mysteries and exceptions. As for the words "pomnik" and "zabytek", just like in English one word can have several meanings, so it is similar in Polish. The word "pomnik" is a word denoting an object - it may be a sculpture, a tree or a bush, in which case it is a natural monument. "Pomnik" can be a structure e.g. to honour fallen soldiers, like the Tomb of the Unknown Soldier in Warsaw. "Zabytek" it may be, for example, a historic medieval church, a historic theatre building or an Old Town with historic tenement houses.
I hope I managed to answer your question. I will be happy to answer your other questions. Regards