I have a spare battery which is mint, removed when fitted Odyssea could try that in your car for a bit! been tested and works fine and is still under warranty iirc, just not upto running my stereo etc...
Leds draw such small amounts of current you could connect 4 strings of leds to the dash illumination wires and it would be fine but im anal as you know so would use a relay to pull the power from a chunky cable
Check connectors on power steering pump, i think they make more noise in the winter tbh when they first start, few people have noticed that
Clean battery terminals and alt cables, check earths prob fix the probs!
(FRENCH SHITE!!!)