I want to learn korean! Does anyone want to be my teacher? I already know all the letters! I also know a lot of words like 안녕하새요, 감사합니다, 이름이 뭐예요?, 제 이름은 다니엘 입니다, 고양기, 사과, 코뿔소, 사랑해요, 여보세요, 안년히 가세요, 좋은 하루 되세요. And many more! :-D But I still have a long way to go!

It's 안녕하세요, 제 이름은 다니엘입니다, 고양이, 안녕히 가세요 (there were small mistakes in your introduction:)). Some words are:
family 가족 friend(s) 친구(들) school 학교 animal(s) 동물(들)
Learning Korean might be difficult because sometimes there are different words for the same meaning (it depends on the age of the person you talk to). For example, if you want to say Goodbye, you say 잘 See More 가 to your friends and 안녕히 가세요 (When that person is going away from you)/안녕히 계세요 (When you are going away from that person) to an adult. When an object is plural, you add 들.
There are no 'z' and 'f' pronunciations in Korean:D
Some sentences that might be useful:
I'm Swedish. 저는 스웨덴 사람입니다. May I help you? 제가 도와드릴까요? I'm sorry. 죄송합니다. Thank you. 감사합니다/고맙습니다 (1st one is more polite). Have you ever heard about ~? ~에 대해 들어 보신 적이 있나요?