I'd say get a new battery, although that's just me and I'm not really someone you should necessarily listen to. I know that dimming lights is usually a sign of a voltage drop but I haven't heard of that happening without a powerful amplifier drawing a large load. Also were these issues happening...
Haha I don't know why you're looking here man. The slipping sound indicates that it's mechanically broken so I'd suggest contacting the manufacturer of the CD player or just replacing it. I can't view the video for some reason so I don't know what else to say.
I don't know much about the battery itself but the first thing I'd check for would a short possibly caused by body damage ie the chassis somehow got in contact (after the crash) with the positive battery terminal or a component that shorts it and drains the battery constantly.
Just bringing up a little problem I have with the aluminium foil. Personally I wouldn't cover the electrical parts with a material that conducts electricity itself.Because although it may stop water from getting and staying in the components, unless you disconnect the battery there is a danger...
Yeah that's the ground wire, just cut off the connector at the end and solder the wires together. I've noticed that a lot of pre-2000 Mazdas have their ground wire like yours. I replaced a HU on a 97 121 (bubble) and it had the same dealio.
This is probably far too late to matter but why sell them? just use the ones your boss gave you in the front (http://www.msprotege.com/forum/showthread.php?123629472-How-To-Installing-different-sized-speakers-in-your-car).
As far as the rear speakers go I wouldn't dump them, definitely you want...
So I've been working on the sound system in my 2002 Protg for a while, and at about $700 (Australian) I think it's about time to start showing off. Although I am definitely not finished...
So far I'm running...
-120WRMS 10" sub (Sony Xplod XS-L1030). Which I managed to pick up for $20 off...