substained alternator abuse

your best bet for your problem would be an H.O. alternater but there is not one for that car and caps are junk so i would suggest a kinetik battery and some fabrication to make one of the larger ones fit your car www.kinetikaudio.com 

Easiest solution would be turn off the loudness button.  By nature, Loudness only works at lower volumes & tapers off as you turn it up.  The idea is to accentuate the bass & treble at lower volumes when they're less noticeable, then "dissolve" once you give it more juice.  That's why your problem disappears at higher volume.

If you like the sound of "loudness," then by all means keep it & go with a new battery - that's a good start.  A capacitor would be a good idea imo because it will lessen your headlight dimming problem.  Some people think they're worthless, others swear by them.  I believe they're great for solving problems like yours.  I don't think they do much of anything for overall sound quality tho, and in that respect are waaaay over-rated as marketing hype - I imagine BT would agree.  It will definitely help with the headlights.

a cap  is like putting a band aid on a gun shoot wound  is just not enough it would help with the headlights because caps give your amp less power because they add more resistance  also don't give up on the alternater yet call all the local auto eletric shops and if you find a guy that knows what he's doing the shop can take your stock alternater and rebuild it with higher output

Yes a cap is a band aid - sometimes that's all you need tho.  No it doesn't give your amp less power or increase the resistance, unless you're talking about the added resistance of a connection point atop the cap (which is virtually nothing),  that's just asinine.  If you're actually concerned about those issues, wire it downstream of the distro block.  It's basically just a reservoir.

If I'm wrong on those points, someone show me the physics.

Which tells us one of two things - Either the laws of physics didn't apply at your local SPL comp, or you & your friend did something wrong.

I mean seriously - that's the only basis for your broad, sweeping conclusion that "caps are junk they don't help they suck power and add resistance to your amp"?!?