Mostly if I see tattoo's, kanji for martial arts, kanji on katana, etc. I only see Kanji, I never see any hiragana. for those things, do japanese just write down what they want and erase the characters that ain't kanji? or is it something else?
The latter. Those words are written according to their own grammar(e.g. the order of kanji) that is basically same as Chinese. Actually, those are often from classical Chinese or 漢文.