You're close! Except for no. 3 - it's Guidraco. And you're right about Thalassodromeus & Istiodactylus.
As for why Princess Tetrapod is a pterosaur... well the Ice King spoof is certainly part of it. More crucially, azhdarchid pterosaurs are one of the many TetZoo 'mascots' - along with babirusas, tapirs, cassowaries, and the like. So it was natural that the princess of the tetrapods should be one.