When I turn on the headlights, I have.

With the multitude of problems that are likely related, first check if the front running lights are on. I'll bet they are. If so, suspect bad grounds on the rear light bulb sockets. If you use a test light or voltmeter at those lights, you'll find full 12 volts on the brake light wires when a helper is pressing the brake pedal, and you'll find 12 volts on the tail light wires. The problem is you'll also find some voltage on the ground wires. They are terminals that slide into an opening on the side of the sockets and they commonly get corroded. You can buy replacement terminals from the dealer's parts department but that doesn't address the corrosion inside the socket. Your best bet is to buy new sockets from any auto parts store or find some nice corrosion-free used ones from a salvage yard, and wire them in.