#2
They turn on and off the coil split function on the pickups. They are worth having if you want to have a single coil-esque sound on tap.

NOTE: It will NOT sound exactly like a single coil pickup
#3
The push pull knobs split the coils on the pickups giving them the sound of single coils.

And yeah, they're worth having. They make the guitar a little more versatile.
Jackson DK-2 [2004 MIJ] (EMG 81/SA)
Jackson RR-3 [2007 MIJ] (EMG 81/60)
Ibanez RG370DX [2009] (EMG 81/60)
Epiphone Les Paul Custom [2004] (EMG 81/85)
Ltd/Esp M-17 7-String [2013] (EMG 81-7 set)
Bugera 333XL 120watt Tube Head, Crate BV412 Cab
#4
As much as I love this guitar, I don't feel the split coils are worth having (Because of the pickups). If the pickups wern't active it would probably be worth having.

Overall it's a good guitar but I wouldn't exactly call it versatile.
Schecter C-1 Hellraiser Fr
Peavey 6505+ 112