1) -나 and -(으)ㄴ가 - A) pose a question to oneself or no one in particular, as in wondering or lamenting to oneself, B) ask a question of someone younger than you.
Usage (B) is now becoming less common, except the "-나요?" form which is popular ("광화분행 버스는 어디서 타나요?").
Of the two, -(으)ㄴ가 is more formal and used more in writing, while -나 is common in everyday situations ("얘는 왜 이렇게 안 오나?").
2) -니 is a colloquial question ending which may only be used with children or close friends. It is similar to -냐 (not 나), another informal question ending which is more masculine sounding than -니. Both sound very casual, direct, and specific (they can't take the -요 politeness suffix), compared with the more general question form -아/어?, although they're all more or less the same in meaning.
- 나는 왜 그떄 말하지 못했던가 [못했나]? Why didn't I say it then? (question to oneself)
- 그렇다면 삶에서 제일 중요한 건 무엇인가? So what is the most important thing in life then? (general question)
- 어디 가니 [가냐]? = 어디 가? = Where are you going?
- 이거 네가 그랬니 [그랬냐]? = 이거 네가 그랬어? = Did you do this?