[Who resolves the push on SWORD base]

With the new wording on  S.W.O.R.D. ESTABLISHES
BASE ON MOON’S BLUE AREA who resolves the push? 

It says the winner chooses the character, but then adds the line about the opposing player resolves the push.  Is that the opposing player to the winner, or opposing player to the character chosen?

[X-force/spider foes leaderships + multiple activations in a turn?]

Are x-force/spider foes leaderships once per turn, or once per character per turn?

Trying to parse the difference in wording between these 2 affiliations, and why they are different.