Is it permissible to remove pubic hair for someone whose menstruation began in Dhul-Qa'dah, and who will cleanse herself and go for Hajj?

There is no harm in removing pubic hair in the last days of menstruation before Ihrām, as this is one of the Sunan (traditions) of Ihrām. As for after Ihrām, it is not permissible to remove any hair or nails until the first Taḥallul (exiting the state of Ihrām). Sheikh Ibn Bāz issued a fatwa permitting the trimming of nails and combing of hair during menstruation.