Audio CD is markedly different from other removable media. In fact, it does not contain files and the data stored in raw samples of fixed format. Thus, you can not just copy the audio files on the disk - it will not recognized by the player. The quality of sound Audio CD often exceeds lossy formats such as MP3, but inferior to lossless formats like FLAC and APE.
A .CDA shortcut file is a small file generated by Windows for each track on a n audio CD. The file contains indexing information and are named in the form Track.cda. The files contain no audio and are basically useless when a CD is ripped to a computer's hard drive or converted to MP3 and written out as files to a CD.
If your car audio decoding does not support MP3 files or if you have high-end CD player, then to make audio cd you will need to specialized software, such as Audio CD Burner. It decodes the audio files on-the-fly to raw samples and writes them to disk. If your file type is not supported directly, you can convert audio files before burning. To maintain high quality would be nice to have WAV files with Stereo, 16 bit, 44 100 Hz.