Can you Barrel Through an enemy that was just displaced by H3xx3r's Unlimited Power tactic? If so, can you Barrel Through an ally that was just displaced by an opposing H3xx3r's Unlimited Power tactic? I'm inclined to say yes, but since Valkyrie's Frostbite is not considered a "roll targeting Maximus" and therefore cannot be stopped by Adamantine, I'm not sure. On the one hand, Barrel Through's conditions are a bit different. "Immediately after a Target's displacement" just seems to mean when any Target is displaced, and enemies are targets, as opposed to Adamantine that needs a "roll targeting Maximus" and it's not exactly clear that the roll is targeting anyone in Frostbite's case. On the other hand, it was ruled that Valkyrie's Frostbite has no targets, so it would seem like Unlimited Power also has no targets, since the wording is very similar.
Valkyrie's Frostbite does not need a Face-to-Face roll (it's a normal Action ─green─), so Maximus is not a target for that roll. If I'd write Frostbite again it should be something like "2 - Frostbite // Impose the Inmobilized State to every Adjacent Enemy". With no Range in declaration it should clearer there is no target for this Action. Unlimited Power is not about a roll, but an effect: Displacement. The requirement for Barrel Through is not being a target neither a roll, it's just to be displaced. Then yes, you can Barrel Through a char when displaced by Unlimited Power.
H3xx3r's Gotcha action doesn't need a face to face roll either, but if you use it on Maximus isn't it targetting him?
But Gotcha! requieres a Target. You need to be within Range (and LoS) and its effects and Switch require both a Target.