It's great (and unusual here) to see such a detailed and complete first post, with voltages marked, even!
This is definitely possible, but not simple.
I have little experience with automotive audio. Others on this forum probably have more. Also you should do some Googling for some of the keywords I mention here. I'll tell you what I know.
First, you will need to deal with interference and surges on the automotive +12V rail. It would be best to do this outside the player because electromagnetic interference is notoriously difficult to contain.
The filtering and clamping is done in stages. First a varistor such as the V18ZA40 (
http://www.digikey.com/product-detail/en/V18ZA40P/F3078-ND/1009327) to clamp the load dump voltage, then probably an LC filter, then a regulator with a wide input voltage range.
You will need regulators to provide accurate and stable voltages to your player's circuitry. There are two types of regulator: linear and switching. A linear regulator will only drop the voltage, and can't boost (increase) the voltage. A low-dropout linear regulator needs only a small input-output differential voltage, usually less than a volt. For example a typical low-dropout linear regulator with 12.0V output would need an input voltage from 12.5V to 40V for correct regulation.
The automotive supply may be lower than 12V so even if you use a low-dropout linear regulator your 12V output may be too low for the circuitry to operate reliably. It's probably designed on the assumption that the 12V rail will be reasonably accurate. You can get buck-boost regulators that can do either (they are switching regulators). Some people get these from eBay where they're widely available.
The 5V rail can be obtained from the 12V rail using a linear regulator or a "buck" switching regulator. Switching regulators generate their own switching noise, and filtering with capacitors (and sometimes inductors) may be needed on their inputs and outputs. Although the switching frequencies are way above 20 kHz so people can't hear them, the supply can produce "sub-monics" at lower frequencies that you can hear.
Also you'll need to generate a -12V rail, presumably using a switching regulator with a negative output. These may be available on eBay as well.
It would be handy to have some idea of how much current the player draws from each of those rails. You can get a rough idea by cutting the wire from the power supply to the player main board and connecting an ammeter (a multimeter set to measure current) across the break. Make sure you exercise all the player's functions including all the motors. You might want to simulate a jammed CD; this will increase the current drawn by the player. Then add 50% for safety. (Engineer's fudge factor.)
Then you know the voltage rails required, and the currents that the player will draw from each of the rails.
The automotive environment is inherently very noisy electrically. There are guidelines for physical positioning, and connection of earth returns, to minimise noise. You may have trouble with ignition noise being coupled into the amplifier. Inserting inductance (actual inductors, or just ferrite beads and ferrite cores that you wind the wires around) may help.
Do lots of research and read forums related to automotive audio. Good luck!