As for varying movesets and normals per char for each mode, that remains to be seen. But really, are any of those normals gonna be as good as auto-heat? And from what it looks like from certain chars only, HM normals / movesets = FM normals / movesets.
It has been seen. And in fact in general it seems that they were given inferior moves, normals and options compared to the other style to balance it out. H-Hisui is just like C-Hisui with her most important tool stripped from her, and H-Akiha is lucky that her new j.C is so buff cause that's all she has really and she's been severly lacking in terms of mixups so far. H-vAkiha lost her j.C knockdown so now she has to rely on airthrow which are much less effective, and the loss of pits for pressure doesn't do anything good for her either.
Now this may not be true for every characters, but it certainly is for a few of them.