First , I would like to say a big thx you , to Amir , for the free work hs is putting into this great community.
The component you are discussing about is a ..."simple" common mode choke , used a lot on analog devices they are slowly disappearing as part of the "cost cutting drive".
Next (with blue pots) is a very smart design called a "capacitance multipler". It drops the DC voltage about 1.5V and it removes noise by up to 50db (0-20Khz) (PSRR) on your DC power. Yes you can use up to 31V on Volt+D
The output filter on Amp is NOT a datasheet copy(not TI design). We spent a lot of time finding optimal values and fine tuning the output filter, we have much , much more filtering the normal datasheet .
I think that one of the reason why people find Volt+D to sound good...is the noise reduction on the output filter. I am fully aware that it should not matter, and yet it is my opinion that it does. I have no hard data to explain it but this output goes direct to speakers. Very good speakers have zobel networks and such that remove the HF noise (attenuate it) but most speakers have substandard (or none at al ) filters and somehow some of the hi frequency finds the way to your ears. (again no hard data but its what I think and design to remove it)
Note that I do design using a AP machine but I do not get guided by only THD+N at 1Khz. I pay attention to other (measurable) data and try to attenuate.