Can the CD-ROM drive in use as a car CD player reproduce MP3 files?

No.  If not connected to a computer, the CD-ROM drive will only work to play audio CDs. Music CDs in the MP3 format are recorded in the CD-ROM format. To read it, the unit forcibly needs to be connected to a computer.  MP3 songs are not played by the CD-ROM drive, but rather by the sound card of the computer, and the machine processor is responsible for transforming the MP3 format into an audio format.  Car CD players that play MP3 have a dedicated processor capable of reading the CD-ROM format and of converting MP3 files into audio ones. Since the common CD-ROM drive doesn't have such processor, it can not play MP3 files.

Can the same adaptation be made so CDs may be played in a domestic sound system?

Yes.  To do so, the sound system must have an auxiliary input channel.  However, to prevent the sound from getting distorted, you will have to use the audio output at the back of the CD-ROM drive and nor  the earphone output, as mentioned last week.  To do this, you will have to take the audio output cable from the CD-ROM drive and solder two RCA plugs - a black or white one (left channel) and a red or yellow one (right channel) – at the end that should be connected to the sound card of the computer. If you don't know how to do that, contact an electronics technician. To feed the CD-ROM drive you may use a power source from an old PC.  One important detail:  AT power sources have an on-off switch, but the ATX ones don't.  If you will use an ATX power source, you will have to make a pin-14 connection (green wire), from the main plug of the source to any black wire to turn it on.

Won't the CD oscillate too much?

That will depend on the unit used (its manufacturer and model). Of course you cannot expect a CD-ROM drive to have the same stability of a car CD player.  Remember that our tip is to assemble a car CD player spending nothing (or almost nothing).  If you used our tip it is because you are possibly not willing to buy a car CD player.

Why should the connection between the CD-ROM unit and the amplifier be made using the ear phone output and not the one at the back of the unit?

That is because car amplifiers don't usually have volume control.  If you use the output at the back of the CD-ROM drive – which doesn't have volume control either – the sound from the amplifier will always be at its loudest. We believe that this is not convenient.  If you should use the output at the back of the CD-ROM drive only if you are to connect it to a pre-amplifier, equalizer, mixer, or home sound system, since they have volume control.