If you wirte as you want, write this, 철수는 자신이 잘할 거라고 생각해요.

(저는) 제 친구가 행복'하'다는 것을 알아요. ( ) is OK, If you want to write or not. 하지만 다음 "말도 맞는지" 잘 모르겠어요. 불확실'함'이 있기 때문이죠. ( I think, you don't need to write these words. It is just repeating.) (저는) 제 친구가 행복한 지(를) 알고 싶어요. If there is something that you don't understand yet, plz reply.

4 examples is all correct. But, most Koreans prefer 가장 to 제일. 제일 is 한자 style.

I gave you a msg! plz check this :)