Which loc are you using? Most new ones are automatically turning on and have an rem out to use. If not, use the car’s ACC that turns on with the key. If you experience “thumps,“ you may need a replay to isolate the 12v source.
Second battery only helps when you turn off the car. If you are concerned about current draw, upgrade your alternator. To maximize your stock alternator, use large or oversized OFC copper wires.
Adding a subwoofer to a Stock equalized system can be problematic if not done right. If you tapped the stock subwoofer speakers you could be experiencing the stock system cutting out the low frequencies. JL Audio‘s new LOC combats this some, as does the Audio Control Pro LOC. You may want to try...
May want to check your ground, even re-ground if using factory ground. Then, check all connections and for consistent voltage. Finally, pull it out and test on the bench. if it does it on the bench, it’s defective.