in audio every setup ever HIDs has solved dimming head lights. The ballasts act as a buffer. Every local setup that complained about dimming headlights that did HID swaps solved their dimming issues. A lot of people on this forum and many other forum already knows its one of the best solutions especially if your volts arent dipping down to 10s and 11s.
multi-meter. I highly doubt it or else you'll have a much bigger problem on your hands then just dimming. If possible just add a 2nd battery to the back parallel to the 1st battery since your main battery is extremely tiny. They should help you maintain some loudness without totally screwing over your electrical system. Big 3 upgrade should help as well.
PS you do NOT need a high output alternator for a friggen 1600 rms total setup. I ran way more than that on my stock 80 amp alt on my 03 corolla with lots of batteries. Just have your battery reserve on point and big 3 and you can run almost 3-4k. You have people try to overcomplicate and tell you how sh*t works on paper trying to make you overspend while in practice, you can make things work with a lot less. Its not 100% optimal but its 100% doable.