I will shoot this piece in the face if I have to listen to it one more time.

This is a pretty easy to follow sonatina with clear exposition, development, and recapitulation sections. Okay, let's start out the harmonic analysis.

Exposition ms.1-15
First Tonal Area: C Major
ms.1-3 I
ms.4 V, HC
ms.5 I
ms.6 I, V6/V
ms.7 V, vi6, V64, V/V, transition
Second Tonal Area: G Major
ms.8 I
ms.9 V6
ms.10 I
ms.11 V43
ms.12 I6
ms.13 IV
ms.14 V
ms.15 I, PAC


Development ms.16-19
New Key: c minor
ms.16 V42
ms.17 i6
ms.18 V65, i
ms.19 V, HC
Retransition ms.20-23
ms.20 V7
ms.21 i64
ms.22 V6
ms.23 V


Recapitulation ms.24-end
First Tonal Area: C Major
ms.24-26 I
ms.27 V
ms.28-29 I
ms.30 V7, HC
ms.31 I, transition
Second Tonal Area (transposed to tonic key)
ms.32 V6
ms.33 I
ms.34 V43
ms.35 I6
ms.36 IV
ms.37 V
ms.38 I, PAC

Pretty simple right?
Now, to answer questions c, d, and e...
The theme from the first tonal area is "explored" in the development. Really all that happens here is that Clementi takes the first theme, which is in major, and makes it minor, pretty straightforward. The harmonic motion is also simple it goes D,T,D,T, and then back to Dominant one last time ending on a half cadence.

Nothing really drastic happens when the two themes return in the recapitulation. The first theme is in its original key but is lowered by an octave. The second theme is also the same...minus the it being transposed to the tonic key part.

Yep, this is a sonatina. And yes, a sonatina is a basically a shortened sonata. And yeah, it does have an abbreviated development section. Is there really anything else to say? Well, I suppose you could say that if this were a sonata then perhaps the development section would have elaborated a bit more on the first theme, as well as developed the second theme, and maybe even the development section could make up it's own theme for itself! yay for run-on sentences.