Is it possible to apply for a chinese tourist visa and how do i get an alien registration card?

You can't get an alien registration card because you are on holidays in South Korea. The Korean ARC is issued to aliens who work or reside or study in South Korea for a long time (at least more than 6 months).

If you have been Mainland China in the last 2 years and can provide the previously used China visa and entry record on your passport, it is still possible for you to get a single entry China tourist visa in Korea even though you don't hold a Korea ARC with at least 6 months validity.