Going to the first question. The statement has merit. Bottlehead transformers are wound with shielding, still they are as far away from the audio circuit as possible in the layout. If your piece with the outboard power supply has the transformer near the audio circuit the same thing applies. Otherwise the umbilical would be 4" long.
I would guess that most power conditioners are well shielded. However, you have power cords, try it. First put a meter across the speaker leads, turn up the volume control so you get some reading on the meter. Then move the outboard power supply or conditioner away from the audio components. See if the noise level drops.
Seems easy enough and really cheap to try.