The first movement is a basic Sonata form, ABA. The A section is mm.1-78, starting in gm and modulating to BbM. I marked measures 1-8 as an introduction. The B section is mm.79-168 and I marked this section as being in cm and fm, modulating to GM as it leads into the return of the A section. The A section returns at measure 169 and continues on to the end in the key of GM with a codetta measures 193-197.
The second movement is Theme and Variations form; however, I think that this movement could possibly be a double variation form because the first and second theme appear to be in different modes (theme I, Major; theme II, minor). Another reason I think this is a double variation piece is because of the placement of the Major and minor themes: Since the Major theme opens the piece, the variations are ordered in such a way as to close with the Major theme. The theme is introduced in mm.1-10. Variation I is mm.11-22 in the keys of bm and EM. Variation II is mm.23-37 in the key of em. Variation III is mm.38-51 in EM, and Variation IV is mm.52-59 also in EM.
In the second movement, there is an interesting chord in measure 8, G dominant 7. I think that Haydn uses this chord to possibly poke fun at the fact that this quartet piece is in gm, and to "reminisce" on the close of the previous movement, which ends in Gmajor. What do you think about measure eight and the role it plays in this Haydn quartet?