Some hydrogen peroxide should make your scratch plate sparkle white again, you'll find it online cheap enough and an aluminium baking tray from Asda to pop it in.
I'd leave it out of the way of where it could spill/tip over, from sunlight and definitely away from children/pets.
Should only be a few pounds to do, that and some nail varnish will cosmetically do the trick.
The J pickup shouldn't be too hard to resolve. If it's not an issue with the knobs or wiring, then a replacement J pickup is never too much to replace these days.
http://www.entwistlepickups.com/pickup.php?puid=JBX