If I use Gladion and choose to put Jirachi {*} into my hand, can I use Jirachi {*}'s "Wish Upon a Star" Ability?
Sorry, but Wish Upon a Star only triggers when you are taking it as a face-down prize card, not when you are trading it with another card.
Source: TPCi Rules Team (2018-08-02)
If I use Gladion can I choose Greedy Dice from my prizes and play it right then?
Greedy Dice can be played only if it's taken as a face-down Prize card. Gladion doesn't count as "taking a Prize card."
Source: TPCi Rules Team (2018-03-01)