autozone battery tester gone crazy

Ok, I have a 96 chevy monte carlo ls. I have stock battery and stock alt. I am running a kenwood kdc-4022 HU to factory speakers, a RF 5002, 2 10" MA Audio dual 4 ohm voice coil in a sealed box wired in a 2 ohm load and a 1 farad RF cap. The amp and the cap are powered by a 4 AWG power wire. ( I know, I know....cap is not needed in my case but I had it laying in my house ever since I bought from a garage sale for the great amount of $20 bucks. So I figured I might as well use it.) Whenever I hit some major bass notes and really loud, my car lights will dimm (headlights, domelight and dashboard lights.) I went to autozone to check my battery and my alt. and the machine showed that my battery was being charged but it showed .8 amps. The guy said that it was really weird because the battery was being charged but the machine was showing only .8 amps from the alternator. He said that his machine was doing something weird so he said that I should take my alt. out and get it bech tested. Here is my concern. I am really lazy to just get the alt.  out to get it bech tested and for the guy to say "Ohh your alt. is ok", so I am thinking maybe he was just not that smart and did not know how to hook up the wires correctly, he seemed to have a hard time trying to get a good ground, so maybe that's what it was, but at the same time, my battery WAS getting charged correctly so wouldn't that show that my alt was working? I am going to do the big three, since I have not upgraded my battery gorund cable to a 4 AWG, I am still on the original ground wire.

Should I just eliminate the cap? will I loose bass response if I do this? maybe I should get a HO alt. Is there a HO alt. for my car? I heard those can damage teh car. I am just really confused. What do you think?

Also when I step on the brakes my front speakers make a little "pop" noise. I removed the head unit and installed the factory one and the problem stoped, installed the kenwood HU again and the noise was still there. No idea what could it be. if it was the ground, wouldn't it make the noise even with the factory HU? It can't be the amp, because I am not running any speaker on an amp. So I am going crazy for this one 2. Any input on this? Thank you.

2 10" MA Audio dual 4 ohm voice coil in a sealed box wired in a 2 ohm load

How do you get that?  One sub per channel at 2 ohms/ channel?  Amplifier output 150 watts X 2.  (CEA 2006).  online spec sheet

I am going to do the big three, since I have not upgraded my battery gorund cable to a 4 AWG, I am still on the original ground wire.

You've got to start here and get your system fine-tuned.  There's some things amiss with grounds, wiring, gains, impedance loads....something besides too much power draw. 

Build the box so that it performs well in the worst case scenario and, in return, it will reward you at all times.

Sorry about the 2 ohm, typo, I have them at 4 ohm.