Are Anya and Nina the same person? No
They can't be the same person, they're from different Universes.
They are both the daughter of Magneto in their respective universes. However, Anya died at a young age and has no known mutant powers, unlike Nina, who seems to have the ability to communicate with animals.
Is anything else known about Nina's powers? Kind of.
We don't have any info on Nina's exact powers, but there is a character in the Earth-616 universe with similar powers, Lin Li (aka Nature Girl).
Lin Li had the power to communicate with and control not only animals, but plants as well. If Nina's powers are the same as Lin's, then once she matures she will also have power over flora and fauna, though it's quite likely that Nina only possesses the Fauna half of those powers.