What is the legal ruling on dealing with the "mortgage" banking system, which is based on paying a sum greater than the price of the house, or dealing with Islamic banks that buy and sell according to the fluctuating market price, in order to secure suitable housing?

Purchasing homes via the mortgage system in Europe and Western countries is definitively the very essence of forbidden riba (usury/interest). It is riba al-nasi’a (interest on deferred payments), the prohibition of which is undisputed. It is not permissible to embark upon it, no matter how great the Muslim's need, except in a case of dire necessity where his life depends on it. Allah obliterates riba and blesses that which is lawful.