The problem with copper foil is that if you use adhesive strips, and overlay them, there's no electrical connection from strip to strip. The adhesive acts as insulation. So I've heard - I've only used paint.
Depends on the copper foil. The ones that are designed for shielding (as opposed to decorative uses) have adhesives which are conductive enough for the purpose. Plus, even without that, the adhesive just acts as a dielectric, making the pieces into a low value capacitor that will be completely open to the AC signals you are trying to block.
There is a lot of nonsense on the internet about shielding guitars, and it is just that - nonsense. It really is a very simple thing, and the conditions inside a guitar are really very forgiving. You don't have very minimal amounts of current, and the impedance of everything is relatively low compared to the input of the amplifier. It's a bit different for acoustic pickups/preamps, because the impedance of the pickup is so high, but on an electric guitar any method of shielding it will be just fine. As long as you actually DO shield it, of course. Copper foil, aluminum foil, shielding paint; it just doesn't matter. In the real world, you will never notice a difference. I find shielding paint to be easiest, but as I said earlier that is in large part because we shield a lot of guitars at the shop, and so it make financial sense for us to buy a can of shielding paint. You need to do at least two coats of the stuff, by the way. But we've done them with aluminum foil and spray adhesive, we've done them with sticky back adhesive too. They all do the job just fine.
Gabriel