"I don't envy gods, they meet only once a year" likely refers to the Chinese folklore that is associated with Chinese Valentine's Day, in which a goddess (or a minor deity) came into the carnal world and fell in love with a herdsman. It is forbidden for a goddess to fall in love with a mortal. Anyway, in the end, the punishment was that the goddess (Zhi Nv 织女) and the herdsman (Niu Lang 牛郎) were only allowed to meet once a year, on a bridge made of sparrows.

At risk of being politically incorrect (since China is officially atheist): in Chinese culture, the concept of reincarnation is quite popularly accepted.

Full disclosure, the author of this translation is not 100% sure about "After this depart, who knows what will happen." But it's probably right.

"karma has not been settled" is a shorthand way to say: good deeds have not yet been rewarded, and bad deeds have not yet been punished.

"If the gods were irrational, they would age too" means that the difference between mortals and gods is that gods are rational, instead of showing favor or love that goes against self-interest, even to the point of being ruthless if really needed.

This song is NOT trying to make a statement regarding monotheistic god or whatever, especially since plurality is not very explicit in the Chinese language.

"Using a thousand years, I exchange for the next dynasty" likely means I exchange for "the next dynasty" with "a thousand years" of my time