If my father in law takes out the mortgage for the house I am buying, and I am paying the monthly payments (from income of the basement+) is it ribbis?
It depends on the circumstances. If the house belongs to you, and it is under your name, but he took out a mortgage which he essentially is obligated to pay, then it would need a valid heter iska, otherwise it would be ribbis. However if the reason he took out the mortgage is because the house is in his name, and essentially he owns the house, and the mortgage payments are the rent that you are paying him to stay in the house then it would not be ribbis. This is because he didn’t give you a loan, and you are only paying him for the use of the house.