Quoted:
If you have dimming headlights, you're taxing your electrical system too much.
The solution doesn't lie in a capacitor.
There really isn't much (if any) practical use for a storage capacitor in OP's system.
Incorrect.
There is nothing regulating the voltage to the headlights. Therefore they will dim naturally when the voltage of their power supply drops. Going from the 14.4v that the alternator supplies under a small load to a perfectly normal 12v that it might supply(with the battery backing it up) under a medium load will cause the lights to dim and there is nothing wrong with that. "Too much" would be when the voltage in your vehicle starts dropping to ~10v or less.
You are right about the capacitor though. They really aren't needed. Amplifiers have enough capacitance built into them to handle the dynamics of music. If you are exhausting your power supply adding a capacitor will only increase the demand on the power supply and lower your voltage potential.
As for the original posters "2400w" its really only 1010w RMS. Not much power at all. Shouldn't require a power supply upgrade unless the vehicle has a very small alternator. The 0awg power is overkill for that. Nothing wrong with that but a 4awg wire would have been perfectly fine unless you had like a 25ft run of it.