Stacking Critical Threat Range (TR) with Focus Attack?

Question

Please note that PC is an Aegis using Martial Maneuvers, Level 9 and has a BAB of +9/+4 and has the Greater Unarmed Strike, Two Weapon Fighting feat and Improved Critical feat among others

Focused Attack (Combat)

You can concentrate on a single attack to improve your chance of scoring a critical hit.

Prerequisite: Base attack bonus +6.

Benefit: When you take a full attack action, you can choose to make only one attack. This decision must be made before making your first attack. For every attack you could make but don’t, the critical threat range for the one attack you make increases by 1. This increase happens after all other adjustments to your critical threat range. Thus if you could make three melee attacks with a keen scimitar as a full attack, when you use Focused Attack you take a full attack action to make a single attack with a threat range of 13–20 (18–20 for a scimitar, 15–20 for a keen scimitar, 13–20 for giving up two attacks with Focused Attack and a keen scimitar).

and

Broken Blade Stance

The disciple of the Broken Blade has learned the flows of combat to a degree and has the insight necessary to see the path to victory through the patterns of steel his opponents weave before his eyes. While in this stance, the initiator gains a competence bonus equal to his initiator level to Acrobatics checks to avoid attacks of opportunity, and may make an additional attack when making a full attack action. If the initiator is two weapon fighting, he gains this extra attack for both hands. The attack(s) uses the initiator’s full base attack bonus, plus any modifiers appropriate to the situation.

1. Reading Broken Blade Stance, my Level 9 Aegis should have a full attack bonus of +9/+9/+9/+9/+4
2. Focus Attack says make one attack, any sacrificed attacks add +1 to critical threat range for the one attack. I my Aegis has a single attack of +9 and threatens on 16 out of 20.

3. How does Improved Critical factor in? Does the "doubling" of a weapon's critical threat range? Is it just double the weapon's critical threat range then factor in Focus Attack and the stance?

   EX: Greater Unarmed Attack 1d8 TR 20x2 = +9/+9/+9/+9/+4 to hit 1d8 damage TR19 with Focused Attack and Broken Blade Stance = +9 1d8 damage TR15x2

4. And, most important, is this legal and or broken?

Answer 1

The feat Focused Attack says, "This increase happens after all other adjustments to your critical threat range." Thus the threat range adjustment from the feat Focused Attack occurs after the threat range adjustment from other sources like the feat Improved Critical.

For example, were the question's aegis—that's two-weapon fighting and that possesses the feats Greater Unarmed Strike and Improved Critical (unarmed strike)—armed with his unarmed strike and a dagger, he could take the full attack action, forgo 4 attacks, and make with his unarmed strike 1 attack that has a threat range of 15-20: from 20 to 19–20 via the feat Improved Critical (unarmed strike) then forgoing 4 attacks to increase the unarmed strike's threat range by 4 more than that to 15–20.

(Note that even if a weapon has a threat range of 1–20, typically an attack must still meet or exceed the target's AC to threaten the critical hit unless the attack roll is a natural 20 then the attack must be confirmed normally, needing to again meet or exceed the target's AC unless the critical roll is a natural 20. A large threat range alone does not guarantee striking and dealing damage.)

Whether the third-party feat Focused Attack and the third-party stance broken blade stance are legal in your home campaign is something to discuss with the GM. Exceptional cases notwithstanding—like when making an attack with a weapon that possesses a magic weapon special ability that only activates on a confirmed critical hit or when making a particularly devastating magical touch attack—, I'd rather make multiple attacks than just one scary one, but I have terrible luck, and maybe yours is better.