If someone bought a car from an interest-based bank and then sold it to another person, does the second person bear any sin if they use the car's price to pay the installments owed to the bank?
When the buyer purchased the car, it became their property, and the price became their responsibility. The bank acts as the seller's agent for receiving the payment. Therefore, there is no sin on the second buyer, God willing, as long as the bank does not impose an increase in the amount if a payment is delayed. And Allah The Almighty Knows Best.
Is it permissible to distribute the raw meat of the vowed animal sacrifice amongst the poor/to offer it to them in cooked form?
It is impermissible for the vow-maker to eat from the vowed animal sacrifice, rather, he/she should distribute it as he/she had intended upon making the vow, but if the vow was a general one, without any specification then, it is better to give it as raw meat.
Is it permissible for the wife to give the Zakah (obligatory charity) of her money to her poor husband?
Yes, it is permissible for the wife to give from the Zakah of her money to her poor husband. And Allah Knows Best.
Is it incumbent on the fiancée to obey her fiancé?
When the woman settles in her husband`s house, it is incumbent on him to provide for her and it is incumbent on her to obey him. Before that, and if the marriage contract had been concluded, then she is lawfully his wife and thus she should abide by custom in treating him, but if the marriage contract hadn`t been concluded, then she should treat him as a non-Mahram (Marriageable).