Is it permissible to purchase a house in a method where an institution participates with 75% of the price and owns 75% of the rent, and is it permissible to borrow from a friend to pay the remaining 25% in exchange for giving him 25% of the rent until the loan is repaid?

That process is permissible if the institution is a partner with a percentage equal to what the buyer paid, and then the institution leases its share of the house to the buyer. However, lending to a friend with an increase is not permissible, because it is a loan that draws benefit.