First of all, the notion that Bill Kristol was "single-handedly responsible for her nomination" is absurd. There is no evidence of that. He was a McCain supporter, and that was about all he was. I don't recall him being all that enthusiastic about her in August 2008.
The facts are that several McCain factions either wanted Lieberman or some other moderate to be the VP choice. Sean Hannity and Mark Levin have stated that they (and they mentioned Rush as well) lobbied hard for months to get Palin the VP slot. In either case, it was McCain's final choice, and not the popular one within his campaign.
Kristol wasn't shell-shocked. He said that maybe Palin is more "crazy like a fox" and that this may well be a very "shrewd" move on her part. He seems fairly supportive of what she is doing if she wants to seriously run.
As for why she communicates via Twitter and Facebook, she is taking advantage of modern communication techniques and bypassing the media filter. Winners try to communicate in all different ways with common, ordinary people to get their message out. That is common sense politics.
As for Kristol, just because you're ignorant of any "evidence" of his support, means nothing. He was talking up this "incredible Governor from Alaska" on FOX, a full year before the nomination and reports I read said he met several times with McCain to get him to consider her. No one in the McCain camp knew Alaska had a governor.