Is it permissible to pray for the prolongation of a person's life, and is it valid to pray that Allah take from the life of the supplicant and give it to the one supplicated for?

It is permissible to pray for a long life. It is preferable, however, to qualify it with what benefits the person being prayed for in their religion, such as saying: "May Allah prolong your life in His obedience." Indeed, it is authentically reported that the Prophet, peace and blessings be upon him, prayed for a long life for Anas ibn Malik, may Allah be pleased with him. As for a wife asking to take from her life and give it to her father, there is no need for this. Allah is capable of prolonging the father's life without taking from anyone else's life. It is also recommended to supplicate for the sick with what has been authentically reported in the Sunnah.