Just a minor technical clarification: Wounds in this system count up, not down, as in Hit Point driven systems. A character does not become incapacitated or suffer a critical injury until the Wound Threshold (WT) has been exceeded.

In the above example, if the character chooses to use advantages to inflict a critical injury on the opponent, and the opponent's WT has also been exceeded, then the GM can simply announce that there is an additional +10 to the percentile roll, in addition to any other modifiers. If the player elects not to utilize advantage to inflict a critical injury, then the critical injury roll could be announced once the rest of the Advantage/Triumph has been spent and their effects are resolved.

New question: If a critical injury is inflicted due to WT being exceeded, do the qualities of the weapon that caused the threshold to be exceeded (vicious, etc.) and the talents of the character wielding that weapon (Lethal Blows, etc.) also apply to the critical injury roll?

Just a minor technical clarification: Wounds in this system count up, not down, as in Hit Point driven systems. A character does not become incapacitated or suffer a critical injury until the Wound Threshold (WT) has been exceeded.

In the above example, if the character chooses to use advantages to inflict a critical injury on the opponent, and the opponent's WT has also been exceeded, then the GM can simply announce that there is an additional +10 to the percentile roll, in addition to any other modifiers. If the player elects not to utilize advantage to inflict a critical injury, then the critical injury roll could be announced once the rest of the Advantage/Triumph has been spent and their effects are resolved.

New question: If a critical injury is inflicted due to WT being exceeded, do the qualities of the weapon that caused the threshold to be exceeded (vicious, etc.) and the talents of the character wielding that weapon (Lethal Blows, etc.) also apply to the critical injury roll?

If the hit results (taking the target above WT) are considered part of the hit, then I'd agree that the weapon qualities should be used in the crit roll. However, it seems weird to me that the damage results of the hit are resolved before the advantages and triumphs (and the crit they could buy) are resolved. I'd think that all aspects of the hit (including rolling the crit bought by advantages or triumphs) would need to be fully resolved before the target surpasses WT and gets the going unconsious crit roll.

Although I can see it working that way too. The acting character announces the damage and what they plan to spend advantages and triumphs on, including if a crit would be activated. Then the hit damage is resolved, which would take the target beyond WT. Then the crit is rolled and the GM tells the player to add +10 to the roll for knocking them out. It does make crits simple and call for less dice rolls.

What this does is it makes characters with Lethal Blows or Disrupters more deadly for PCs. Just knocking a player beyond WT means that a Disrupter weapon will automatically get the beefy crit roll. The GM can't decide to not activate the crit through advantages or triumphs, it happens automatically. Could get deadly.