Yeah, screw the bolt back in, so you have something to hit to knock the wedge loose.
Trainers wear out tires quickly, but these ones are probably pretty dry anyway (looks can be deceiving), so when the rear wears out, rather than putting on a new tire, put the front tire on the rear. Then buy a pair of tires, but put a new tire on the front only, By the time _that_ rear tire wears out, the new-ish front tire will have very little wear (just the repeated 2-mile round trip). That will be the best way to use up whatever useful life those tires have.
Option - if you have a bike co-op in your area, find another cheap rear wheel with a freewheel, and keep it at your friend's house. Buy two new tires for these wheels, and put one of these old tires on the other wheel, to use on the trainer. You'll still have one more trainer tire to wear out as well.
Double-check the brake pads as well. Old pads, even if they show little use, can be dry and hard, making them poor performers.
Is your mention of black a reference to repainting the whole frame? That would not look good. And you wouldn't want to lose the branding just on account of some nicks and scratches. You can experiment with mixing Testors paints, literally a droplet on a toothpick at a time, to get the right shade of blue.