I meant that it was composed with the intent of the Scherzo being followed by the Adagio. Not just that he happened to compose one movement before another. The musicological analysis, of which I am not capable myself, would back that claim up.
Yes. In fact, it was initially published in that order, before the composer decided to reverse the two movements before the initial performance. It's a little misleading to talk about "all of the performances" Mahler gave, because the first round was such a flop and the reviews so vitriolic that it's only a slight exaggeration to say that the Sixth Symphony was the straw that broke the camel's back and forced Mahler to leave his job at the Vienna Court Opera.
As for the order the movements were composed in, like several of the other symphonies, the Sixth was composed from the inside out. The inner movements came first (forget which was the first, probably the Scherzo) then the first movement, then the last, but with the structure already more or less formed in Mahler's mind from the beginning.
The reason being given for Mahler's change of heart after the GP and before the first performance was that it was suggested to him by people he trusted that the first and second movement were far too similar; that the listeners would respond better to the fast-slow-fast-FINALE structure.*
*That may be true: but I happen to believe that this is the point of the symphony: A ONE, TWO Blow to the kisser courtesy movements 1 & 2. Then recovery and hope in the Adagio. Then the devestating Finale. What the Scherzo-as-second movement loses following the similar First, the Finale loses trice over, following the Scherzo-as-third.
I think it's helpful to look at the work as being in three parts: the first movement, the inner movements, then the finale. This way the piece functions whether the scherzo or the andante follows the opening allegro.
The first movement presents a conflict between two types of themes; let's say the strident and the lyrical. The whole movement inverts the normal dramaturgy of a sonata-allegro form, with the highest tension at the outer points and the lowest tension in the exact center. In the end, the lyrical theme takes hold, but only by taking on the characteristics of the strident theme.
The two central movements re-examine what just occurred, focusing on separate aspects. The scherzo takes up the strident theme type and in fact goes over the same harmonic territory as the first movement all over again, with the exception that it ends in wearied collapse. The tension in this movement more or less stays at a high level. The andante takes up the lyrical theme type (though actually derived from a more martial sounding passage from the first movement) and takes the key of the lowest point of tension from the first movement as its home. The development of tension in this movement is something like the first, but less gradual, with mercurial shifts in mood. The climax near the end marks the point at which the conflicts in the music throughout rise to the surface, and it is resolved with seeming forthrightness before ending in wistful recollections of some of the earlier motifs (the movement's "theme" does not return after the climax).
A tonally ambiguous gesture sets the finale into motion, and its drama stems from constant and almost regular waves of tense striving and uneasy meditation. The main themes of the movement combine characteristics of both the strident and the lyrical types from the opening allegro, and the finale turns at those points where the orchestral setting becomes most opulent in the Straussian vein. As with the andante, these will always collapse, and here they do so with violence. We find that the triumph of the first movement's coda cannot be recaptured and the interior movements pointed towards the ultimate conclusion of the work in defiant destruction.
