The diversity of your symptoms could suggest the body processor module...
That unit governs much of the 'behaviour' of the car's electrics, including wiper logic.
It's hidden underneath the passenger knee bolster, it's the biggest electronics 'control box' on the car and easily recognised by its large amber-coloured multiplug.
Picture of the module with cover removed:
Check the connectors for dirt/corrosion and check the module's insides for any water ingress.