How do I download a YouTube video to play on my DVD Player in my car?

You need a simple program like this http://www.vso-software.fr/products/convert_x_to_dvd/ it is called convetXtoDVD, very easy to use, drag the video in the program, with a blank dv-r and it will make a DVD. To your second question, it depends on the quality of the original video. Good luck.