Na 나 is referring to I or me, Dangsin 당신 is referring to you. But we don't say 당신 between friends. Neun 는, eun 은 are Korean postpositions which come after the subject.
는 comes after 나, 너(means you, you can say it to someone younger than you.) usually ends with a vowel or double one.
은 comes after any noun like 동생(it's a general term to refer to younger brother or sister), 선생님 teacher usually ends with a consonant or double one.
I watch TV. Naneun TV-reul bonda. 나는 TV를 본다.
I eat a hamburger Naneun hembugureul mungneunda. 나는 햄버거를 먹는다.
Eul 을, Reul 를 are also Korean postpositions which come after the object.
을 comes after any noun like 동생, 선생님 usually ends with a consonant or double one.
를 comes after any noun like 오빠 older brother or one's boyfriend, 언니 older sister usually ends with a vowel or double one.
I've hit my younger brother(or sister) Naneun dongseng-eul dderyut-dda 나는 동생을 때렸다.
I love my older sister. Naneun Unnireul sarang-handa 나는 언니를 사랑한다.
Haeyo = Do
Gongbuhaeyo? Do you study? 공부해요?
Neh, gongbuhaeyo. Yes, I study. 네, 공부해요.
Woondonghaeyo? Do you exercise? 운동해요?
Neh, woondonghaeyo. Yes, I exercise. 네, 운동해요.
Hope this helps.