All the braided wires will be for ground, the centre core (white insulated) will be your signal.
In the case of that red wire coming off the pickup, they obviously cut it too short to reach the switch so joined it (really badly) to get the extra length. Whilst the exposed bare portion might not cause any problems if it contacts the shielding, it's bloody poor workmanship to leave it like that. They could have at least wrapped some tape on it!
Your ground wire coming from the bridge can be soldered to the back of either pot like the ones already attached there.
The braided wires from each pickup will get soldered to the single lug on the switch where the braided portion from the black wire is already soldered as well.