A few different models of Lighsabers are Cumbersome or Unwieldy, if someone is using one of the dueling specialty Talents (Makashi Duellist for example) and using an alternate characteristic than Brawn because of it, would that alternate Ability be used to reduce or negate the Cumbersome/Unwieldy trait of the weapon?

Example, a Soresu Defender stylist with a WP of 5 is using a Double bladed lightsaber, and has the Talent of Soresu Defender, allowing him to roll his WP for all Lightsaber rolls. Would his WP be used instead of Brawn/Agility for the Unwieldy/Cumbersome trait of the weapon?

No, Cumbersome and Unwieldy are locked into the characteristics they tie to.

For instance, big guns with Cumbersome still require you to have high Brawn to wield without penalty, even though all of them use Agility for their combat checks; same with heavy or awkward lightsabers.

There is a talent that allows low brawn people use big guns and mods:)

A few different models of Lighsabers are Cumbersome or Unwieldy, if someone is using one of the dueling specialty Talents (Makashi Duellist for example) and using an alternate characteristic than Brawn because of it, would that alternate Ability be used to reduce or negate the Cumbersome/Unwieldy trait of the weapon?

Example, a Soresu Defender stylist with a WP of 5 is using a Double bladed lightsaber, and has the Talent of Soresu Defender, allowing him to roll his WP for all Lightsaber rolls. Would his WP be used instead of Brawn/Agility for the Unwieldy/Cumbersome trait of the weapon?

Nope.

If the lightsaber you're using has Cumbersome or Unwieldy, then you need a Brawn or Agility score equal to that quality's rating to avoid the penalty. Which means a PC using one of those lightsabers isn't going to be able to focus exclusively on whichever characteristic happens to tie into the LS Form spec they've chosen.

Especially for the case of Unwieldy and double-bladed lightsabers, this is a game balance concern. Linked 1 on a lightsaber means that it's going to be very easy for a PC to score a second hit, especially once their dice pool includes 3 proficiency dice (which is stupidly easy to obtain by the time a PC gets their hands on a lightsaber). A basic lightsaber is bad enough since it's got Breach 1, which means a hit with it is going to leave the target hurt. A double-bladed lightsaber is two hits, and a simple Aim maneuver gives the attacker a boost die, upping the chances of getting the advantage necessary to trigger that additional hit, which in turn enables the PC to largely obliterate minions and rivals with ease.

Thanks a bunch, makes sense to me, especially regarding the game balance.

Don't forget that Enhance can eventually allow committed Force dice to raise your Agility and/or Brawn for the purposes of meeting the requirements of Cumbersome and/or Unwieldy.