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.
Should a pregnant woman who broke fast because of pregnancy make it up, and is a ransom due on her?
The pregnant and the suckling, if they fear for their health, may break their fast and make up for it, and no ransom is due on them. However, if they broke fast in fear for the fetus and the baby, then they are obliged to make up for it, and pay the ransom which is feeding a needy person for each of the missed fasting days. And Allah Knows Best.
Is it permissible for us to sever ties of kinship if our blood-relatives` gatherings/meetings involve acts of sin?
Observing kinship ties is obligatory, and paying your blood-relatives a visit causing their sinful acts to be hindered , then you should do so. However, if their sinful acts continue while you are at their gathering and they didn't respond positively, then observing kinship ties via telephone and the like will suffice in this case. And Allah Knows
Is it permissible for a woman to leave her house wearing brightly colored clothing?
Brightly colored clothing is of woman's adornments, however; and this shouldn't be revealed save to her husband and Mahrams. And Allah Knows Best.