A. No. According to a major yoghurt manufacturer, you would have to leave the yoghurt in your car for 24 hours at a temperature of 100°F or 37°C or higher to kill the 'friendly bacteria'. The average trip home of 15 or 20 minutes would not do that. Still high temperatures may cause the total number of bacteria to decline.
Ideally you should bring your refrigerated items home in an insulated carrier bag and pop them straight in the refrigerator. And try to buy from a supermarket with a big turnover so you're buying yoghurt fresh with the maximum live bacteria.