1) Yes, both parts of the pickup should have a fairly solid foam rubber block underneath it. You need some springiness in the support for the pickup so you can raise and lower the pickup height so I wouldn't use solid wood to get the height right otherwise there's no adjustment. Just first check that you haven't missed the loose bit of missing foam somewhere in the packaging and if you can't find it, I'd drop an email to adam at PBG and he should sort you out with a new bit of foam asap. adamboyle@pitbullguitars.com
But you can normally get similar thickness foam in larger sheets from eBay which are better value (especially if you ever plan to make more guitar kits).
I don't think that the two pieces of foam on one pickup are supposed to be shared between both pickups, as there doesn't seem to be enough depth to just one of the pieces shown.
2) The spare black wire is a grounding wire for the bridge. You should see an angled hole under where the bridge will sit. During final assembly, you'll want to push the grounding wire up the hole in the control cavity so it pokes out where the bridge goes. Then bare a couple of cm of the wire and splay out the strands. This then gets sandwiched between the body and the bridge to ground it to stop the strings acting as aerials for electrical noise.
Last edited by Simon Barden; 26-02-2019 at 11:58 PM.