1) Many of us lease. If you do, unlike most cars the residuals are low so rather than giving the car back at lease end , you can trade it in and get the equity that is the difference between the residual and the dealer trade in price. I got $6k when I traded my 2010 in on a 2014. If you do plan on keeping the car long term , an extended warranty is a good thing to have. Don't buy it initially. Anything can happen. Buy it anytime before your manufacturer's warranty runs out. If you intend to keep the car for some time, buying is the better option
2) I'm on my 3rd B8 S4. Never had clunking or banging with any of them.
3) Thermostat failures should be fixed, but there still seems to be occasional reports of failure. It will be covered under warranty if it does happen.
4. a clutch, if you have a 6MT will not be covered under warranty. Brake pads, wiper blades, front end alignment and tire rotations , are not covered either. Many of us have AudiCare which covers maintenance and service during the factory warranty.
5) S4s can be purchased for as little as $500 over invoice based on the dealer. You should get a better deal on a leftover 2014. If not, Go somewhere else or get an 2015 which will be worth more when you resell it.
6)IMHO, This is a great car. I've had 3 of them because I cannot find anything else out there in the price range that I like better. All 3 have had few minor issues. If you are expecting the reliability of a Japanese car, you may be disappointed. Also, DO NOT BUY THIS CAR if you think it is going to get good gas mileage. You will be VERY disappointed.