Is it permissible for my seven-year-old son to lead me in prayer, and is it permissible for me to lead him in prayer given that he is my son?

The imamate (leading of prayer) of a discerning boy is valid, based on the Prophet's ﷺ saying: "The one who is most knowledgeable of the Book of Allah should lead the people in prayer," and the story of Amr ibn Salama, who led his people in prayer when he was six or seven years old. So, if your son fulfills the conditions, pillars, and obligations of prayer, there is no harm in him leading you. However, it is not permissible for a woman to lead a boy in prayer, because he is considered like a man. What is permissible is for a woman to lead other women in prayer.