What is the ruling on buying a car through Murabaha from an Islamic bank that is affiliated with an interest-based bank? Is Murabaha considered a circumvention of the religion? What is the legitimate alternative to it? And what are the rulings on installments and contemporary Riba (usury/interest)?

The decisive factor is the content, not the names and titles. So, if a bank calls itself Islamic, it is not truly so unless its dealings are in accordance with Islamic Sharia. It is not possible to issue a ruling on a specific bank without examining its regulations, laws, and mechanisms, and this is not our function. A previous answer addressed dealing with an Islamic branch of an interest-based bank, and Murabaha sale is Islamically permissible, as is installment sale. One can refer to the mentioned fatwas to understand the forms of Riba (interest/usury).