I don't think she's a telepath. She knows a lot about it from her line of work and from being married to Oliver. This is ambiguous enough to potentially read her as a telepath, but that fits into the ambiguity of the show.
They haven't explictly said whether she's a human or a mutant. Enough is not known about her back story that if they wanted to decide she's a telepath and have her directly demonstrate those powers.
Melanie reminds me of an older, kind Emma Frost and I think this similarity is deliberate. Wonder if she knows Charles Xavier and the X-Men?