I have a variable sparging technique that is usually chosen batch by batch. I generally am looking at grain bill amount, how thin/thick the mash is, gravity of the beer, and even to some extent the style of the beer. I'll pick my poison based on what I'm feeling is the appropriate choice for that particular batch. These changes all came about because of a series of beers that had this very subtle astringency that wasn't always obvious. Since making these changes I have not been experiencing the astringency. The compromise I've chosen to accept is a slightly lower efficiency than I was getting before (84% brewhouse previously vs 80% brewhouse now). This is still an experimental process for me and I'm only now starting to have a guide as to why I would pick one process (or combination of processes).
As for your questions:
1) I initially chose to perform a single batch sparge with half of my sparge water. The remainder went directly into the BK. This has transformed into a sliding scale based on the several factors I listed above.
2) I treat all of my water with salts/minerals/acids - mash and sparge - the same as I would for a "traditional" sparge.
3) Undetermined. Of the styles I've brewed since making this change, my approach has worked well, but I have not brewed dark beers since the change; however, I suspect this will be beneficial for dark malty beers.
The processes I use are basically:
-No sparge; all sparge water directly to BK
-Single batch sparge with various amounts of designated sparge water
-Sprinkle sparge (the term I use; could be called pseudo-fly sparge) with typically 1-2 gallons
-Combination of the two immediately above
As I said, it's still in an experimental stage of development for me but, for me, I'm seeing better quality beers. I understand and accept that Denny is better than I can ever hope to be, but still I try