The intention is that donations to charity don't have income tax applied to them. When you donate an object like a car it's not really the same - most likely you bought it, got your money's worth from it and now want to be rid of it, so it's not really like you're donating something you paid income tax on.
You paid income tax on the money used to pay for the car. By donating the residual value you are recovering part of the income tax that you already paid.
Yes, but for many people I suspect the value to them is much lower than the auction price. If you were following standard accounting like a business you would probably have fully depreciated the car before the time came to auction it.
