The longer answers, courtesy guitarelectronics.com:
What is the difference between 250K & 500K pots?
Either 250K or 500K pots can be used with any passive pickups however the pot values will affect tone slightly. The rule is: Using higher value pots (500K) will give the guitar a brighter sound and lower value pots (250K) will give the guitar a slightly warmer sound. This is because higher value pots put less of a load on the pickups which prevents treble frequencies from "bleeding" to ground through the pot and being lost. For this reason, guitars with humbuckers like Les Pauls use 500K pots to retain more highs for a slightly brighter tone and guitars with single coils like Stratocasters and Telecasters use 250K pots to add some warmth by slightly reducing the highs. You can also fine tune the sound by changing the pot values regardless of what pot value the guitar originally had.
What is the difference between Audio and Linear taper pots?
Audio and Linear taper pots have the same total resistance but differ in which position of rotation the pot will reach the 50% value. Linear pots are usually marked with a B or Lin (examples 250KB, B250K, 250K Lin) and will reach 50% of its total resistance in the 50% rotation point. Audio taper pots are usually marked with an A or Aud (examples 500KA, A500K 500K Aud) and will decrease most of the resistance in the last 50% of the rotation. This can give a more gradual audio reduction is some cases. Most manufactures and builders either use Audio taper pots for volume and tone or linear for volume and audio for tone. However, if a problem of exists where a volume or tone pot has no effect on the sound, try a changing the taper. How to check the taper with an ohm meter: Set the pot to the center position (50% rotation) and measure the resistance between the center pin and each of the outer pins. If the the resistance is equal (50% of the pots value) the pot is linear. If the values are not equal, the pot is an Audio taper.
What is a Fender TBX tone control and how does it work?
Some Fender guitars come equipped with a special pot called a TBX Tone Control T (treble) B (bass) X (Cut) that cuts either treble or bass instead of a tone pot that cuts treble frequencies only. This is done with a ganged 500K-1M ohm control pot that is wired to work as a low-pass filter in one direction and a high-pass filter in the opposite direction. A center detent in the middle position is provided for the off or "flat" position. Although Fender altered their Start tone configuration to have the TBX control the middle and bridge pickups, it can be also be wired as a master treble/bass control. The TBX can also be used in place of any standard tone control on any guitar.
How does the tone capacitor value affect the sound of the guitar?
Most guitars and basses with passive pickups use between .01 and .1MFD (Microfarad) tone capacitors with .02 (or .022) and .05 (or .047) being the most common choices. The capacitor and tone pot are wired together to provide a variable low pass filter. This means when the filter is engaged (tone pot is turned) only the low frequencies pass to the output jack and the high frequencies are grounded out (cut) In this application, the capacitor value determines the "cutoff frequency" of the filter and the position of the tone pot determines how much the highs (everything above the cutoff frequency) will be reduced. So the rule is: Larger capacitors will have lower cutoff frequency and sound darker in the bass setting because a wider range of frequencies is being reduced. Smaller capacitors will have a higher cutoff frequency and sound brighter in the bass setting because only the ultra high frequencies are cut. For this reason, dark sounding guitars like Les Pauls with humbuckers typically use .02MFD (or .022MFD) capacitors to cut off less of the highs and guitars like Strats and Teles with single coils typically use .05MFD capacitors to allow more treble to be rolled off. Keep in mind that the capacitor value only affects the sound when the tone control is being used (pot in the bass setting) The tone capacitor value will have little to no effect on the sound when the tone pot is in the treble setting.
Does the number of control pots used affect the sound?
Yes: Since the load on the pickups is determined by the total parallel resistance of all pots that are being used at a a time, using fewer pots will reduce the overall load and give a slightly brighter sound. Also, connecting more pots is the same as using lower value pots, two 500K pots will loose or "bleed" the same amount of treble frequencies as one 250K pot. To lessen the effect, switching should be designed (when possible ) to remove pots from the circuit when the related pickup is not selected. An example of this is the Les Paul: bridge controls are out of the circuit when in the selector is in the neck position and the neck controls are out of the circuit when the selector is in the bridge position.