I can't tell what that wire is coming from or going to, so not sure what's going on there. If it came that way from the factory, I'd say it's just poor workmanship and needs insulating.There is this bare wired section on the wires going to the switch. The fact it is bare implies it's expected that it will be soldered to something but I'm not sure.
The ground wire for the bridge doesn't need to be soldered, it just needs to make good contact with the bridge plate.Also when earthing to the bridge plate is it supposed to be soldered as well or just placed with bare wire?
This typically achieved by stripping back enough of the insulation so only the bare wire is protruding from the hole in the body. 10-12mm should be plenty.
What I do is splay the individual strands of wire so they can lay flat under the plate. This eliminates having a "lump" under the plate and should allow it to sit flush with the body. The bridge will be tightened down with the mounting screws to apply enough pressure to hold the ground wire in place.