To add a bit to what TimberWolf said:
You can use the site D3planner - Maxroll.gg - Diablo 3 Resource Website Season 27 to see how different skills and bonuses interact.
For example, I imported your profile into D3planner and took some screenshots so you can see why Mirinae does not do that much damage.
Here is a link so you can see the exact same thing that I am using: D3planner - Maxroll.gg - Diablo 3 Resource Website Season 27
It sounds like you are considering why it is better to use taeguk than Mirinae, so I used your profile and compared what would happen if you swapped the gems.
With Taeguk, you average about 27B damage per hit and you get 2.73 hits/s . See the screenshot below for the calculations.
If you swap Taeguk for Mirinae, you lose the 48% bonus to your damage bringing it down to 18.7B.
What you gain from Mirinae is a measly 110M in damage and it only hits once every 3 secs + 15% chance per hit to get an additional smite.
So you lose 48% of your total DPS but gain an average of 155m or .008% more DPS.
The reason for this is because Mirinae does not benefit from the 490% dmg from Ninth Cirri, 200% from the Belt, 200% from the 2 piece bonus, the 15,000% from the 6 piece bonus. So a total of almost 800,000% multiplier is not applied to mirinae’s damage since it is not Hungering Arrow.
Since all of these damages are multiplied together, you can see why making a small change to one piece of gear can make a huge difference.
For example, if you had a Quiver that had 600% Hungering Arrow dmg on it instead of 490% you would go from 26.9B to 50.8B dmg per hit, or 88% more damage from just that one change.
As far as your other question. The 15% from Bane of the powerful is added to your total Elite damage, so it gets added to the 14% on your ring, and the 30% from Aughilds to give you a total of 59% Elite damage. The 20% is a multiplier, so all of your damage is 20% more after killing an elite pack.