i can't really answer those, as I'm not sure of them yet.
i can give some roundabout answers though:
Spoiler:
i'm not sure if sasaki had powers to begin with. i believe she does. my statement that they believe she is the godlike being is pretty much a direct quote, however(the person(tachibana) literally says they think that sasaki, NOT haruhi, is the godlike existence), so chances are either she already does have them or she is a person who is capable of receiving them(vol4 nagato style). sasaki, however, is not ignorant of the 'alternate brigade's' purpose.
i have not heard of a slider yet, and i am of the opinion that it is probably just a misunderstanding and no slider exists in volume 9.
i believe everyone but Haruhi knows of their existence. at the very least, Kyon does, and Koizumi knows about sasaki, so I presume that the other brigade members know what's up, although they may not know that the other brigade is trying to get Kyon to cooperate with them.