Clean your ground connection from the battery, this should hopefully fix the light dimming/idle drop/radio restart problem, if the battery isn't getting a good grounding, then these will all be possible problems. Get the battery load tested and also test the alternator, if the alternator can't charge the battery well enough, idle drop/surge will occur as the engine is trying to produce more power for the alternator to perform better. As for the corner speakers going out, check in the trunk underneath the speakers in the deck, this is likely the sound system grounding out the component speakers, this happens when the metal of the connectors for the speakers touches the metal of the chassis of the vehicle, the sound system notices a ground and will stop playing music through them as a safety precaution. As for the engine idling at the same beat as the music, you might be dealing with a battery problem, as the music draws amperage from the battery if the battery doesn't have enough to give it will rev to charge the battery, refer to my explanation for testing the alternator/battery earlier, same reasoning. I presume by "to the beat of the music" you are referring to the bass of the music? If you have a subwoofer and amplifier hooked up this is most likely your main suspect for most of these problems. If not, like I said, test the battery, test the alternator, if all fuses are fine remove the head unit and check for if wires are stripped/corroded and possibly grounding, check for grounding connectors on the speakers, and clean your battery ground connections. And also make sure your leads to your battery are not corroded and are snug and large enough for a good connection. Only thing I didn't address is the window rolling up/down. My only thought on this is possibly the window regulator could be going going gone, or very possibly the switch is going bad on the drivers side panel. I am no expert in this situation, but I can say I have had almost all of the other problems happen before on my car.