I would say that for things that have broad mythological definitions (like pixies as you mentioned, or things like vampires or dragons, etc) it's fine to narrow down your definition to characteristics that are present in a particular pop culture media to make it more defined, as long as that pop culture media isn't really, really heavily [i]changing[/i] the folklore of the creature, if that makes sense.  So using dragons as an example, it would be fine to pull from Skyrim or Eragon as a way to better define the type of dragon you mean and their general abilities and characteristics, but you shouldn't use things that are highly specific to that particular version of that creature (such as Shouts or eldunari, respectively). 

As for the witch, that would be fine!  I would imagine they would have a fairly limited understanding and ability to use their powers at the beginning (having to mostly hide them and probably not having a [i]ton[/i] of guidance on how to use them, except maybe from a parent or something), but as a general concept, that's allowed.  It wouldn't be [i]necessary[/i], might it would be encouraged to also give some backstory on why a witch was born on Earth (like, if a parent or grandparent was from Faerie).  But that doesn't [i]have[/i] to be information that's known by the character.