Nah, having the stock radio in the trunk isn't costing you much power. You don't have to have it though, as you can reset those lights without the factory radio. Your owner's manual explains how.

Adding an extra battery won't help with light dimming. Your alternator charges at 14.x volts and when you overdraw the alternator, voltage drops to about 12 volts because that's your battery's voltage, and that's why your lights dim. They are dimmer at 12 volts than at 14. Adding a battery to the trunk will just give you another 12 volt source, so your lights will still dim.

Look on eBay for Iraggi alternators. As far as I know, they're the best high output alternators for the price. When you shop around, make sure to note the output at idle because that'll be one of the most important factors.

 

ok that makes sense but what exactly do you mean by output at idle? for the stock, wouldnt it just be the standard 14volts or 105amps? my cap reads around 14.6ish when i first start the car. but after the car has been running for around a half hour or so, even with the system off or low, its already down between 14.2 - 13.8ish... but alts still good i guess.

 

By output at idle, I was referring to how many amps the alternator produces at idle. Alternator output is dependent on RPMs. The stock alternator only puts out around 20 amps at idle, not the full 105. I honestly don't know what RPM it makes its peak output at. Most high output alternators can do 80+ amps at idle.

It's completely normal for voltage to be higher when you start your car. The alternator runs at a higher voltage for a little while to recharge you battery from starting the car and it'll eventually settle to a constant voltage. For my car, I've seen as high as 15.1 volts on a cold start and usually settle down to 14.4. Every car will be a little different.