The tern 'non-syllabary alphabet' is an oxymoron. 'Non-syllabary writing system' is more accurate. And of course hanja (kanji/hanzi) are still used in South Korea, if only for very restricted purposes.
I see, so Takeshima and Japan are just names for the same thing, is that what you are saying? And China claims Senkakushoto, but the majority of Taiwan’s territory is not disputed, right?