1. Modeller3D will never be as powerful as Blender or AOI,

And you shouldn't try! If someone needs those extensive features then those are the programs to use. Your plugin should offer the basics so that most users don't need to step out to those complex programs. Those basics are difficult enough to implement as you have found out.

2.1 I selected all the side edges.
2.2 I subdivided all the edges.

You are right. When the diagonal edges are split too and those center points are included it works as intended. I'm not used to that because Blender initially has quads and doesn't require those extra splits and points. That also keeps the face count lower.
What you showed works, so no problem there. I just have to remember to include diagonals for division.

2.4 I selected the top 4 vertices and used Inset several times.

I didn't use inset because I wanted only two sides, not all four. But it does work very nicely.

3. What's the issue with the textures?

No issue, but it will appear with more complex models and changing faces. As long as it doesn't show up no worries.

4. About coordinates. The plugin displays the coordinates of the first selected point (even if edges or faces are selected). By modifying the displayed coordinates, all selected points/edges/faces will be modified accordingly based on the difference between the entered values.

Ah, now I understand. You MOVE all selected points relative to the first selected point. A very nice feature but not what I expected! I expected the changed value to be set for all selected points like in Sweet Home 3D. You should find a way to have both options: select move or set. The option of setting the same value has a very good reason, it allows points to merge (remove double vertices). And merged points creates merged edges which are important for correct smoothing. (Remove the doubles!)

The current version already offers the most used/needed features.
I managed to remove a side of a cube by deleting the diagonal edge but it should be possible to remove individual faces (but keep the edges that are shared with adjacent faces)

wishlist
import existing objects (if necessary you can limit it too models with <1000(0) vertices)
Create a face by selecting two edges or three points

For a much later version:
curve edges (like walls in Sweet Home 3D: multiple splits in the edge to simulate a curve but allow the user to increase the number of splits for a smoother curve).
round/bevel selected edges