Q: Dash, Tail/brake, dome, trunk, glovebox, and door lights won't work, dash doing weird things.

So everything was working the night before, it snowed that night and I went to start my car and my dash lights don't come on, my blinkers in the front and back don't work, my taillights and brake lights don't work but my reverse lights and front lights (high and low beams) both work, my dome light doesn't work, my glove box light and trunk light don't work, when I open my door the red light on the door doesn't turn on. All the lightbulbs were recently replaced and I checked all the connections and everything is plugged in. My rear defroster also doesn't work. When I turn my car off, my gas tank needle doesn't go left, it goes right and when I turn the car back on it'll shoot left and then go right and my speedometer and rpm gauge go all the way to the right and then back left. I took it to AutoZone thinking my battery was bad, they said it indeed was but when I bought a new battery it didn't fix the problem, so my question is what is wrong with all my lights?

My car has 113100 miles.
My car has a manual transmission.