What is the ruling of Islamic law on buying a car from a bank through "Al-Amanah" financing, which claims to be Sharia-compliant, and then selling it to obtain cash for building a house, knowing that the bank buys the car and sells it to the customer in installments after they choose it from the showroom?

It is not permissible to deal with usurious banks, because it falls under cooperating in sin and aggression, which is forbidden by Islamic law. The usurious bank does not purchase the commodity with a valid purchase such that it transfers to its ownership; rather, it pays money to the seller and installments it to the buyer with interest, and this is akin to a usurious loan. Even if we assume that the bank purchased the commodity correctly, it is still not permissible to deal with it, because it requires opening an account there, and this is considered cooperation with institutions that openly engage in usury. A Muslim must distance himself from these institutions and seek lawful sustenance, for Allah's bounty is only attained through obedience to Him.