“So I should hear back about two weeks after she does?”
Hear back means to receive a reply or a decision after an inquiry or application. Hear back from someone identifies the source. Tina checks whether her reply should arrive about two weeks after her friend's.
“promise the moon and the stars”
Promise the moon and the stars means to make extravagant promises unlikely to be fulfilled; promise the moon is a shorter version. The official mocks a lawyer's promises, but alien Tina takes the image literally and says the stars are not so far away.
“Complete. First time anyone's said that about me and a form.”
For documents, complete means all required information is present. Tina makes a self-deprecating joke that someone has finally used this word about her and a form. First time anyone's said that shortens It's the first time anyone has said that.