No, we wouldn't, because Sora isn't an official Keyblade master yet. You need to be a MASTER in order to give that power to others, and we know that Sora definitely didn't have that power when Squall touched his Keyblade. As for Jack Sparrow, regardless of Sora's status...do you really think that Jack Sparrow has a strong heart? He's always stabbing people in the back and only truly cares about himself (and a few friends, but he'd never admit to caring about them).
No, the Keyblade did not choose Sora because Riku chose darkness; the Keyblade doesn't care about light vs. dark. It cares about the strength of heart, and at the moment, Sora's heart was stronger.
Kairi's ability was weird in KH2, but now it's been explained. It's possible that she can't summon it herself because she accidentally started the Rite of Succession, but as several people have said before, this could be an interesting plot arc for her.