Definitely NOT Valhalla. I remember Tiger hitting it way left off the tee when he won the PGA there and it went down a giant hill left of the fairway. That picture is tree-lined left.
I'm guessing it's Kinloch. That's a REALLY funky course, it has a lot of split fairways and other odd design features.
#10 no guess. I know of no world class courses in South Dakota.
I'm still pondering the others. #12 is probably going to piss me off because it's going to be one of those new fake-classic courses on Long Island catering to the rich and stupid. It doesn't look like the architecture of the real classic LI clubs, it looks like a Pine Valley copy set on Long Island.
I came up with #11. Won't spoil it, but nobody is going to get it without googling. That course has almost zero public exposure. If you have not played there you've probably never seen it or heard of it.