Hard to say, as far as I remember, it wasn't that what she is is a big secret, per say, but she kept the whole world of mythics a secret from him in general, and he did not learn about them until the start of the game when he moved in.Well, I'm positive she knows, but I'm pretty sure she won't tell you. Esther probably respects your mom too much and wants only that she tell you. That said, given Nefari's investigations and analyses, I assume you'll probably learn one way or another while at the manor.
As far as Nefari's stuff goes, I doubt Esther is truly aware of her research, but I would think that if she asked, and it would help, that she would say, I mean, it would be a big help to her to know what to look for. I doubt Esther knows enough about science to know about double blind studies, to be trying to help that way...
IDK...