re: point [3] - it's more likely that particular guitar wasn't ringing the high "E" very well, rather than the pickup's pole spacing affecting its sensing of it.
It is as you say - improper spacing
looks wrong. But, the pickup's performance isn't affected as much as you might imagine.
It helps to think of the pickup as an inverted transformer.
In a traditional transformer you have at least two isolated coils of wire, commonly called the "primary" and "secondary" windings, which are wound around a common ferrous metal core ("ferrous" is French for iron and its alloys). Due primarily to magic (or, what heathens call "intelligent design"), passing an electrical current through a conductor creates a magnetic field. This field infects the ferrous core. Out of an outrageous sense of entitlement, any other conductors in the area will use that field to
produce a relative electrical current, less some taxation. The effect can be transformative, in that there can be a ratio between the exciting current in the conductive "primary" and the parasitic result in the "secondary" windings. Hence the name "Transformer". Done properly, 12 volts in can be 70,000 volts out. Don't believe me? Pull a spark plug wire off your car's engine, and stick your tongue in the connector while you have a friend crank the engine over. For added fun, do it in the rain in your bare feet.
Hurts, don't it? That'll learn ya. You'll find your gas-powered lawnmower is equally sadistic.
Wrong thinking will be punished. Right thinking will be as quickly rewarded.
Anyway, a guitar pickup works sorta the same way, only instead of creating a magnetic field by passing an electrical current through the primary winding, the magnetic field is already there in the form of a permanently magnetized core. So, now instead of varying the current in the primary to create a varying magnetic field and induce some blood-sucking on the secondary side, we create a varying magnetic field by bouncing the primary winding (the guitar string) around inside a pre-existing magnetic field. The secondary of this goofy transformer is about 5,000 winds of superfine wire. So, we end up with a ratio of 1:5000, give or take a few. Still only produces millivolts, so go ahead and put your tongue on the output if you'd like. No lessons to be learned there.
I said all that so I could say this: sometimes you're the windshield, and sometimes you're the bug.
Wait... that's not it.
Oh, yeah. The magnetic field set up in a guitar pickup's core is fairly broad relative to its height. So, pole spacing isn't as important as you might imagine. I mean, there are limits, but F spacing vs. "regular" (as in
Seth Lover's PAF design) is more of a cosmetic thing than anything else.
