I have a question about the form of each movement, as I have been unable to find this information in a book or online... I that the three movements are Allegro, Andante, Allegro Presto... I have also heard from an unreliable source that the third movement is a set of variations. This is for a music exam I have coming up, and several practice exams ask for the specific form of each movement. If someone knows these that'd be a ton of help, as I've been searching without luck for about an hour and a half lol.
Well...I have played this piece, and I can tell you some generalities. The first movement (Allegro) is Sonata-Allegro form (exposition-development-recap, coda). The second movement (Andante) is roughly A-B-A, but with a lot of modulation, and a cadenza near the end. The third movement is indeed a theme and variations, with the last "variation" making up nearly half the movement.
If you can find Hutchings book on the Mozart piano concertos I think it has more specific form discussion.
Another good book is the one by Cuthbert Girdlestone (I'm not making that name up!). He gives a lot of good details on all the concertos.
The third movement he says is a theme (based on a song sung by Mozart's pet starling!) with 5 variations and a long coda.
The second movement is in 4 sections, which you could call AA'BA''. The B section is in the minor, but the same theme is played at the beginning of all 4 sections.
The first movement is what is sometimes called sonata-allegro, though you need to know that that means something different in a concerto than in a symphony.
In a concerto, the tutti first plays through the exposition, then the piano comes in, and the same themes are repeated, but not necessarily in the same order. And the piano usually introduces some new themes of its own. It's a much freer form than you find in a symphony. And there's always a cadenza between the recapitulation and the coda.
This work was written for a pupil, so it's not as virtuosic as some of the other ones apparently.