How does cooldown reduction work?
Say I'm a Nemesis with Master Lift, the Human Sentinel achievement, two Medical Exo X armor mods, and a Savant X biotic amp.
Passive: 26% CDR
Armor: 46% CDR
Bio amp: 40% CDR
Achievement: 10% CDR
for a total of 122% CDR, but I don't actually have a cooldown of 0 on my abilities, so how does it work?
Additionally, does progress towards squad member achievements carry over through playthroughs? If so, do they have to be unique assignments?
I do not know exactly how the cooldown bonuses work, but I think that they work the same way as damage reduction does (see Weapon and armor calculations by The Grey Ranger). At least that is how I think The Grey Ranger felt that they worked.
But basically, you have the base stat (say 40s from Master Lift). You can get cooldown reductions from your passive, armor (mods), and Omni Tool.
I'm not entirely sure what the exact order is, but let's say they are all 20%
So 40 - 20% = 4- - 8 = 32s.
Then 32 - 20% = 32 - 6.4 = 25.6s
then 25.6 - 20% = 25.6 - 5.12 = 20.48 seconds
But this is just a theory.
The order may be important. So you have:
Passive: 26% CDR
Armor: 46% CDR
Bio amp: 40% CDR
Achievement: 10% CDR
So let's take 40s (Master Lift) as an example and see what we can get:
((((40 - passive) - bio amp) - armor) - achievement)
= ((((40 - 26%) - 40%) - 46%) - 10%)
= ((((40 - 10.4) - 40%) - 46%) - 10%)
= (((29.6 - 40%) - 46%) - 10%)
= (((29.6 - 11.84) - 46%) - 10%)
= ((17.76 - 46%) -10%)
= ((17.76 - 8.1696) - 10%)
= 9.5904 - 10%
= 9.5904 - 0.95904
= 8.63136
Again, this is just a theory. But let's switch the order around to see what we get:
((((40 - achievement) - passive) - bio amp) - armor)
= ((((40 - 10%) - 26%) - 40%) - 46%)
= 8.63136
So apparently that comes out to the same value. Okay. I would actually have to see in-game if Master Lift cooldown is actually around 8-9 seconds though.
And to answer your last two questions, achievements carry over across playthroughs. Once you have an achievement unlocked, it applies to all Shepards.
Since we are on the topic of ally achievements, is the assignment considered completed only if a good outcome is achieved, like for example if I convince Conrad Verner to go home, or anytime the mission is greyed out, like if I get Conrad killed instead due to lack of morality points?
An assignment is considered complete once any outcome is achieved. Using Conrad Verner as an example, the assignment is considered complete whether you convince him to leave you alone (Charm/Intimidate) or if you just tell him to leave at which point he just goes off and gets himself killed. as another example, Major Kyle can be completed if you convince him to stand down (Charm/Intimidate) then allow him to speak to his followers so they disband peacefully, or if you kill him/all the biotics.