Is it permissible to give an unused house to a person in exchange for an agreed-upon sum of money, such that the money is invested and the returns belong to the owner, provided that the sum is repaid without the returns upon receiving the house?

This transaction is impermissible because it leads to a loan that yields a benefit. The man will give you money to use, and then you will return it, and this is a loan. In return, he will benefit by residing in your house without paying rent. A loan that draws a benefit is forbidden, as the Messenger of Allah, peace and blessings be upon him, said: "If one of you grants a loan and the borrower offers him a gift or gives him a ride on a mount, he should not ride it or accept it, unless they had an existing relationship before that."