"Yandere" is a moe term meaning, effectively, "ax-crazy." It refers to a character that will do anything to keep their beloved, including turning a bunch of other potential suitors into frogs to eliminate the ones that aren't who she wants them to be just to make sure there's one less guy in the world that she has to sift through in order to find the right one.
Frog girl has been an interesting experiment. As is perfectly clear in page 9 pan 4, I still haven't quite gotten the hang of her yet (heck, I haven't quite got the hang of Nancy or David at this point).
Originally, the role of frog-girl was restricted to a single chapter. This has been changed; you'll be able to see that in pages 13 and 16, if you haven't already (protip: Land of dreams, Hyperboria, and Mount Voormithadreth are your clues).