Re: How covers and screws effect the sound?
They also shield from some interference, but in a humbucker that is usually overkill. If you make a cover from material that becomes magnetic itself from the magnetism of the enclosed PU magnet you suppress much of the magnet and the tone becomes dull. Even with good ones you lower the height of the resonance peak.
I doubt that the screws that hold the pickup make any serious difference. In general, putting non-magnet iron next to the magnet in a PU (but not between the magnet and the strings) acts as "ballast" and makes the pickup more mellow sounding. Might emulate aged pickups. I'm sure DiMarzio has a patent or five on it. But as I said, the screws holding the pickup are too small and too far away.