The difference between 내가/나는 and 제가/저는 is honorifics; usage depends on who you are speaking to. Speaking informally to somebody your age or younger, you would use 내가/나는. Speaking formally to somebody older, you would use 제가/저는. 은/는 is the topic particle, 이/가 is the subject particle and usage depends on your sentence structure.

나는, 저는, and 제가 all mean I (我). 네가 is you, not I. Actually, only '나' and '저' are 'I' in English, and '는' and '가' are a subjective particle. More exactly '는' is called a topic particle or something else. Anyway, whatever it is named, it is true that one of the '는''s roles is to assign a subjective case to a noun. I won't go into deeper with this matter here. 저 is a polite word of 나. When we speak to the elder or a stranger, we use 저 instead of 나. 제 is a variant of 저. We use 제 when the subjective particle 가 is followed. 저가 (x) 제가 (o)