The chosen unit takes flying steps as if it had the airborneability. If the unit cannot take steps (due to being immobile, for instance), it cannot move to the targeted minion.
What path can I choose when resolving this ability?
What happens if the power of one of the units changes during the resolution of this effect so that it's no longer weaker?
Only check that the target is weaker when it is initially targeted, and when the effect first starts to resolve from the storyline. Once the effect is resolving and minions are moving, it does not matter if the relative powers change after that point.