How do I spell these scales? I know there are three of them, but I don't know the accepted way to spell them. It's an 8 note scale so I assume one note is doubled. Which one?
It will depend on exactly how you are looking at it and what exactly is going on when it is used. Typically, you'll see the 2nd doubled especially when playing over altered dominants like a 7♯9 or a 7♭9♯11 like so:
X: 1 M: C K: Cmaj L: 1/8 C_D^DE ^FGA_B||
The scale itself since it is fairly flexible and you'll get a lot of different combination of vastly different chords through the enharmonic combinations and you'll want the notes of the scale to represent the harmony at that point. So for example if you were playing a half-diminished chord, you wouldn't represent the 3rd note as a ♯2, but instead a ♭3.