Trying to access old un-used brain cells, so forgive me. Many years past when I had audio set ups that used 6 disk CD cartridges (both Pioneer and Alpine) I had encountered a couple of times where the cartridge would not eject; this was primary due to the tray that holds the selected CD not full retracting back into the cartridge. Generally a couple of attempts to eject would work or trying to select another CD from the cartridge to prompt the other one to disengage. If I remember correctly, only once did I have one that would not retract/eject and it required removing the housing to the player and offering a slight assist while trying to eject. Another potential cause is misalignment of the cartridge within the unit...try wobbling it around or lifting it while trying to eject. Failing all of those options, it's possible that the motor has finally failed.
Regarding the red pull out pin with the picture on it...yep, it's the way to apply power to open the frunk to get to a dead battery; read the owners manual for additional details. Also, I see that you are a member from a quite a while back...I'm honestly surprised that you haven't had to use the darn pull out plug to get to your battery. Kudos for owning your car that long and not having to use it. Also, kudos for 13 years.
Finally, that darn wire is obviously not stock, but looks like it isn't the typical botch-job you see posted on here. I would be interested in hearing what you find. Is there anything that is not stock? Is it possible it would have gone to a radar detector? My unsolicited advice is to track it down, and if not in use to remove it before you have an issue where the dead end finds a ground and you end up with bigger issues. Best of luck.