I checked the song you mentioned and I get your confusion, but this sentence was actually not finished in that line. Remember those catchy English songs you may have heard or listened to back when you weren't all that interested in just listening to Korean music, and some of those songs ended several of their lines unfinished, then continues on in the next? This song is just like those. "그 누구보다 널 이해하고 네가" is NOT a finished sentence, and in this song, it is followed by 슬퍼지려 할 땐 그 땐 내가 널 웃게 해줄게, and to sum that all up, the translation is:
그 누구보다 널 이해하고 네가 슬퍼지려 할 땐 그 땐 내가널 웃게 해줄게
When you get sad, I will make you [who is 'better' than anyone] laugh.
내가 is the, let's say conjugated, form of 나 when placed with the particle 가, and 나 means 'I', while 네가, or in some cases 니가, which I kind of think of as a colloquial form, is the "conjugated" form of 너 with the particle 가, and 너 means 'you'. I hope this helped clear up your confusion^^
굿럭~^^