Count Fosco is a vampire.
He's an Affably Evil
, Wicked Cultured Man of Wealth and Taste
. The heroes note he is in extremely good shape for his age and that he even seems to get younger and more fit as the plot progresses. He has a mesmeric effect upon women and can communicate with animals.
The Fairlie family have the X-Gene
Specifically the family mutation gives them prophetic dreams
. In Anne Catherick's case it is more metaphorical, giving her insight into the nature of the people involved as opposed to what will certainly happen. Building off of this, Fosco's interests in the matter were a part of "The Brotherhood's" attempts to gain knowledge or control of England's mutants.