Resolved questions
"나 진짜 가서 자야겠다". Is this sentence correct?

I'm not a native speaker but that doesn't sound right to me.
Whenever you use the 어/아 야 하다/되다 you have to put the 하다 or 되다.
Because of this your sentence isn't correct. How about...
잠이 필요해요.
I need sleep

Betul juga.^^/
Macam mana awak cakap itu dalam bahasa melayu? ^^/


\^o^/

As a native speaker, it sounds good to me. And it also feels like an informal expression, maybe due to the use of '진짜'.