Does a mother's consent for her daughter to go to someone who "calculates with the Qur'an" with the aim of facilitating an engagement and finding a job constitute participation in polytheism (shirk), and does sin result from that?

It is not clear what is meant by the mother's statement that the man "calculates with the Quran," but it appears that the man is asking for the name of the visitor or her mother as part of the ruqyah (definition) (exorcism), and he is among those who seek knowledge of the unseen by dealing with jinn. Therefore, it is not permissible to ask him or believe him. A severe warning has been established regarding asking soothsayers or diviners and believing them. The mother should be advised gently and the impermissibility of her actions clarified. If she does not comply, the sin is upon her, and there is no sin upon the questioner. Consulting soothsayers can, in some cases, be considered shirk (definition) (polytheism).