#2
Cx. A double sharpened C Enharmonically the same as a D, but you'll have to call it Cx in this context
#4
Well, when you look at any (mode of a) major scale, the basic idea behind is that every note should be there, with added flats/sharps as needed, so that no note is there twice. For example, the key of C: C D E F G A B C. You don't call the B a Cb because there's already a C!

The guy asked for an augmented fourth in G#, the G# scale is G# A# B# C# D# E# Fx G#.
You'll see the fourth, which is a C#. To make an augmented fourth out of the natural fourth, we have to sharp it and since that has already happened it becomes a double sharp!
#6
stuff calling it differently, i know youre ment to call an augemented 4th C## or something, but it IS the same as D
:: by the way you know any easy fingerings for aug or diminished chords, or diminished or aug scales?
- tommy