bernie I'm hardly an expert (tdpri will have some super in depth posts on it)
They're staggered to compensate for the radius of the fretboard (strat's are between 7.5 - 12in usually).
They're staggered to compensate for the output of the individual strings (think physics = the thicker a string the more it'll vibrate/resonate).
Doesn't really explain blade or rail style pickups, but then they're usually used on humbucker designs on guitars with a flatter fretboard (16in & up).
Are they adjustable...? Welllllllllll, kinda. Not really. Maybe. It depends. And I wouldn't - unless the pickup was specifically designed to be easily adjusted.
But pickup height IS easily adjusted and - once we put aside the debate over tonewoods and all that - is becoming regarded as one of the biggest influences over tone (and obviously volume). So that is something to play around with - just mark where they are currently before you start tweaking! And bear in mind that they are magnets, so to0 low is a bad thing as they'll pull on the strings (aka “Stratitis”) damping that vibration that actually makes the sound.
Too high means little volume and your lovely toob amp won 't howl at the neighbours like you want it too.