Not so much a loophole as an omission. PRD does not explicitly state that you must have a free hand to "use" the Snapping Turtle Style feat, though I believe that's the intent.
I think you are correct in assuming that you still get a free grapple check as you assert: "it sounds like this would let you get a free grapple check if the guy you're grappling decides to attack you and misses."
And in your third case, yes, an AoO is generally a melee attack, and therefore the "trap" should work as stated.