About the Nogitsune Aura: I'm not 100% sure, but I think I remember that when Derek told the other wolves that Kira is a kitsune and look at her Aura that she's ja "young kitsune" and something like "she has not learned to hide it yet" ~ I could be wrong, but this is how I remember that scene. So if you can learn to hide your aura, I'm pretty sure the Nogitsune could hide his aura, because he seems much older than Kira from the other stories we hear about him.
I agree. If the Nogitsune does have an aura –– which isn’t at all for sure because he’s such a different being in general than kitsune, not possessing (ha) his own physical body the way Kira and Noshiko do for example –– then I wouldn’t be at all surprised if he learned how to hide it. He’s a trickster, after all, hiding and deception are basically his MO. And the characters only saw Kira’s aura at certain moments, not constantly, and I don’t think they saw Noshiko’s at all, which does suggest, even if the show didn’t outright say it, that hiding an aura is something that can be practiced and learned.