As I look over the symptoms, the only common denominator that can cause all of this is a bad battery. OR SOMETHING ELSE THAT LIMITS CURRENT FROM THE BATTERY - so look over the positive battery cable - mostly the smaller cable going to the four-fuse box near the battery, both battery connections, and the ground lug/screw on the battery ground cable as it attaches to the chassis.

I would say "pulse module" but does not explain the spoiler and interior lights acting weird.

I'd swear you have a bad battery OR bad battery cable.