#2
Pots are just variable resistors configured as voltage dividers. Add a poly film capacitor and the pot blends the bass and mids and cuts the treb a bit. They really don't affect the sound in any other major way.
#3
Pots are behind pretty much every knob on your guitar, pedals, and amp. Depending on the way they're hooked up they cut volume, cut treble, cut mids, cut bass, blend between two pickups, or a couple other things. The value of the pot, though, does affect the tone. If you've got a 250K volume (or anything else, really) pot, you can replace it with a higher value pot which will bleed less treble to ground, giving you a brighter tone or vice versa with a lower value.
#4
guitarelectronics.com is a great place for info about these things, you can also buy from there.

guitarnuts.com, blueguitar.org are also really good. lots to learn out there! time to get started