I am eager to improve my speaking skills in Korean and English speaking skills. I am eager to improve my Korean and English speaking skills.

It's correct originally, but with this word order it will sound more smooth (in my opinion

And The more I watch Eric Nam's interview videos, the more I want itmotivated I am. The more I watch Eric Nam's interview videos, the more motivated I am.

"I want it" is okay, but I reworded to make it more clear.

That is whaty I want to take a leaf out of his book. That is why I want to take a leaf out of his book.

So I decided to watch Ted and write summary and my thoughts at least 1 in a week. So I decided to watch Ted and write summary and my thoughts at least 1 in a week.

If Ted is referring to "TED Talks" and not a person, it should be capitalized (I'm not sure what or who Ted is 🤔

That must be worth to do itdoing. That must be worth doing.

I don't know what it is exactly is called. I don't know what it is exactly called.

And I have to take a test,the TOEFL test to improve my English skills and to apply to universities abroad for graduated school. And I have to take the TOEFL test to improve my English skills and to apply to universities abroad for graduate school.

I am not sure what I am going to do but I am considering a lot of selecoptions. I am not sure what I am going to do but I am considering a lot of options.