Green & white wires, right? Those are the wires that tie the halves of the neck pickup together. Absolutely normal. Here's a diagram explaining what's going on. You can click the image for a PDF version suitable for printing.
Click here if the image doesn't display above.
About the bridge ground... If you life the bridge, you'll find the bridge ground wire just kind of laying there. It may very well be embedded into the body after a few yeaars of being clamped down by the bridge. The thing to do is pull a little more length out of the hole from whence it came. Strip off insulation so that you have an inch or so of bare wire. Twist it neatly like this:

and stuff it down one of the bridge screw holes. Re-attach the bridge and you're done here. You might also check in the cavity that the other end is properly soldered to a ground point.
Ken...