Say I'm battling Lusamine in Ultra Space. Her Pokemon has auras, mine don't. Ultra Beasts have auras. I catch them, they don't have auras anymore. Why?
(Also what happens when you release UBs back in the wild?)
Okay, the answer to this question is pretty simple: Ultra beasts have a special version of Beast Boost ability in the wild. As you know Beast Boost causes the most proficient stat to get raised; this for wild UBs happens as soon as you encounter them. The ability manifests itself as an aura around the UB which gets the beast boost effect in battle. However once captured the ability gets suppressed and will only activate after your UB knocks down another Pokemon (the actual mechanism of the ability works now). They lose the auras as now their powers are confined and cannot get their beast boost effect as readily as they want.
As for Lusamine in Ultra Space, if you remember she gets possessed by an Ultra Beast (Nihilego) so the energy or beast boost effect with auras that a UB would receive in ultra space or in the wild, is instead given to her Pokemon as she herself is neither a Pokemon, nor can fight. The Pokemon under her command get the same effect as she would have got if she was a real UB. Let's just say she was a pseudo-UB ;)))
And as for your final question, there are only two ways by which you won't be able to encounter a respective UB in the wild again: Catch them and/or release them. So if you release them, they are gone forever (unless you have multiple of the same one:) )
Hope I helped! :)))