The Ice Ages wiped out most tropical fauna. At that point there weren't many tropical taxa left anyway, as tropical forests disappeared during the Miocene cooling. Those taxa with tropical relatives (Stagmomantis, Mantoida, Thesprotia, Brunneria etc.) re-invaded N-America later.Very fascinating indeed. So if the S. American species "invaded" through N. America, why weren't they able to sustain a population in N. America?
No. I don't know about angustipennis, but aridifolia is a tropical species and doesn't need diapause.Also, you mention that T sinensis doesn't need diapause, so I'm "assuming" that angustipennis and/or aridifolia do.
The latter.And by several other species, do you mean species in the origin area of those three, or species in the same genus that aren't closely related?
Such a thing doesn't exist. The extant species have undergone all about the same time of evolution. The original taxon doesn't exist anymore.One more thing, do you think if speciation did occur, which one (if any of them) would have been the "main" species that the other ones branched off of?