"Opening your mouth when getting mortared" means to keep one's mouth open in the event of a bomb, grenade or other explosion. Explosions create waves of increased pressure, followed by negative pressure, which can be extremely damaging to ears and internal organs. Keeping one's mouth open is said to equalize pressure, therefore reducing internal damage.
In a February 2016 interview with NPR, Kim Barker, who wrote "The Taliban Shuffle," the book that was the basis for this movie, said Tina Fey first became interested in the memoir when Michiko Kakutani reviewed the book for the New York Times. Kakutani said Barker "depicts herself as a sort of Tina Fey character."
During the outdoor night scene with Tina Fey and Margot Robbie next to an open air tent, the harmonica tune from the beach party in the opening of Tubarão (1975) can be prominently heard. It is not a re-creation of the tune, but the same audio used in the movie.
The phrase "no they are just really chapped" (referring to her lip color) was also used 10 years earlier by Tina Fey in her series Um Maluco na TV (2006).