Firstly, here is a great performance of this piece: http://www.youtube.com/watch?v=3izeEp3JKwc
I think these variations, as the workbook questions suggest, are best understood as being paired (or trio-d). Variations I and II go together, as both contain quick, figural 16th-note runs in a neighbor-tone pattern; the first in the right hand, the second in the left hand. Likewise, variations III and IV go together with their triplet figurations (in the right and left hand respectively), both featuring arpeggiation and chromatic neighbors. Variation V is the only one not to have a direct partner, but that's because its variation is character - the very simple rhythm and detached quality make this piece childlike and playful, more like the theme. It is clear, however, that there are influences from the other variations. V is a nice break from what the listener now expects - paired rhythm figurations for each variation - and instead changes the mood and sets up for the next. Variation VI borrows the playful staccato from V in the right hand and the left hand 16th-note neighbor figure from II. It would probably fit best along with Variation II, but Mozart wanted to keep the similar movements separate. Variation VII foreshadows the grandiose twelfth variation with its initial deep left hand and show-offy right hand 16th scalar runs. But this variation is best paired not with XII but with X, because of the 6th-->7th motion sixteenths in the right hand (m. 173-175 and 188-192), which will feature prominently in that variation.
With the next variation, Mozart changes the mood completely, and gets farther away from the theme, with an almost canonical "Minore" variation. Suspensions, chromaticism and foreign harmonies dominate, making this seemingly simple, even childish, piece seem far more complex. I would comsider this a character variation, again, because the change of mode seems to evoke a completely different narrator. This is best paired with the next variation, number IX, because while sounding more simple and close to the theme, it shares the canonical opening and suspensions, although actually back in the major mode (maggiore). Variation X, as I have mentioned, explores the 16th note figure introduced in number VII. This figure stays in the right hand, as the left hand takes over the melody above and below it. Mozart retains chromaticism, sliding playfully through descending harmonies back to tonic (m. 249-264).
Variations XI and XII go together more for character again than for similar figures or ornaments. XI is labeled, "Adagio", and Mozart pours all the aria-like, show-offy Empfindsamkeit he can into it. (The YouTube video performance features not one, but two lengthy cadenzas before the return of the A in measure 281.) This grand and stately character is shared in the final variation, which also works well as a closer because it manages to recap almost every previous variation's figures. The left hand neighbor tone 16ths from Var. II are back, as well as suspensions from Vars. IV, IX and XI, chromatic embellishments from Var. V, and figural/ornamental elements from Vars. I, III and VII. He also adds a large coda, where the closing phrase is reiterated, and then a codetta after that which serves to bring the piece to a grand finish, and the exhilarated listeners to their feet.
This is a great piece, and Mozart manages not to change so much from piece to piece that by the end one can't remember the theme. It's still there, but grandly embellished and played with in a well-organized series of sectional variations. I can imagine Wolfie, smiling, maybe winking at the audience here and there, as he plays this piece effortlessly and charmingly before some royal court.
But that is quintessential Mozart. Especially the wink.