1) Weapons.
2) I'd start by asking the player what definition of Hecate they're using. For an example, there is a canon critter called a "hecatean hag" that shows up in the book "Welcome to the Jungle" - but which may not match the sorts of things your player is looking for. As a note, the player character may not know all the details about who/what they've signed on with - but the player shouldn't be caught by surprise with something like "oh by the way, your sponsor is horribly evil and trying to sacrifice a few small countries for magical power" or whatever.
A normal sponsored magic power is four refresh*, and does not require other spellcasting powers. Curses and shadow magic seems like a reasonably narrow domain; if that's what you want, I'd say, go for it; that doesn't seem like the sort of thing that needs to be more expensive.
*Footnote: Four refresh is if you don't have Evocation or Thaumaturgy; reduce the price by one for each of those powers that you have. So adding a normal sponsored magic on top of a full Wizard template would cost only two refresh, for example.