SK: He didn't know and couldn't imagine that Harry would succeed. If he leaves Harry in the tree, a whole bunch of stuff goes down but the Starborn is in the clear.

PG: Sending Harry to Arctus Tor means that there is a chance Harry could be infected via Lea. I don't think he could predict Molly's ultimate role as Winter Lady.

TC: He wants to get a read on what Harry knows. Harry trusts him at this point and that trust is a more valuable resource to betray later than a possibly botched kill attempt on the Warden of Demonreach.

CD: Exactly, he's going to the battlefield OVER the wall. The way I read it, his eye is a piece of the gate. So, it can do the same function as the gate. I'm guessing that the gate operates even without his intervention. A metal detector will alarm even if there isn't a security agent standing by it.