'I made a bad mistake of selling my car' is wrong. Because you identify the particular mistake, you must use 'the' instead of 'a'. So the following are correct: 1. I made the mistake of selling my car. 2. I made the bad mistake of selling my car.

1. Yes, this sounds fine! 2. I feel like you could drop the "bad" and just say, "I made the mistake of selling my car." But I wouldn't say there's anything wrong with what you have here!

See Answer below.