Hi k, I just read through part 1 of this thread and you said "Sorry... I got confused there cos I was always told by music theory people that one refers to A# as B-flat... (i never figured out why when i asked i was told it was 'just how it is').."
Well, whoever told you that didn't know shit - each note has 3 possible names and you don't have to use one all the time. For example 'A#' is also B flat and also C double flat (you can have double sharps and flats). The reason for this is as follows, as an example I'll use the F major scale.
So you know F major has one black key, but is it A# or Bb? It's Bb - F,G,A,Bb,C,D,E. This is because you don't use the B in the scale, but you do use A so you can't sharpen it in the key sig. Note the continuity in the scale - you never 'miss' a letter out. In diatonic scales you must always stick to this continuity and that's why there are both sharps and flats. Also you can't mix sharps and flats in the same key signature, its either all sharps, all flats or neither.
If we look at your G# major scale, you miss out the A and the E and repeat C and G. It sounds the same as a G# major scale but it isn't
You wrote - G#, Bflat, C, C#, D#, F, G, G#
The real scale - G#,A#,B#,C#,D#,E#,F#(G#).
See how its continuous, no letters repeated and no mixture of sharps and flats. BUT that's a lot of sharps in the key sig (7) and it's fiddly to work with so as a convention instead of calling it G# major we write it as Ab major (4 flats), sounds exactly the same but easier to write and understand;
Ab major: Ab,Bb,C,Db,Eb,F,G,(Ab).
In the same way, E# major (E#,Fx,Gx,A#,B#,Cx,Dx,E# x=double sharp) is exactly the same as F major, but we don't write it that way because it's more effort and harder to understand.
It's hard to explain things and not sound patronising ;-) if I come across that way it's not intentional, just trying to clarify things.