Fuse is not merging shapes' faces

You could use TopExp_Explorer explore(*instance, TopAbs_FACE); to extract the faces from both objects and then fuse those. An alternative may be to compute the intersection (BRepAlgoAPI_Common) and sew the result with the fuse together (BRepBuilderAPI_Sewing). Hope this gives a starting point.

The only code I have is the actual code I use. You can see that on github. https://github.com/WolframResearch/OpenCascadeLink/blob/master/OpenCasca... in that file look for the functions I mentioned in my answer.

It is not clear from your question what do you want to obtain. The result of fuse operation is one shell that contains faces from both arguments, some of which are splits of the original faces. This result is as on the below picture:

May be you want to get merged the result faces that occur to be located on the same plane? It is like on the following picture:

It that case all you need is just to simplify the result. For this you need to call the method SimplifyResult before getting the result:

const TopoDS_Shape b1 = BRepPrimAPI_MakeBox(10, 10, 20);
const TopoDS_Shape b2 = BRepPrimAPI_MakeBox(gp_Pnt(5, 0, 0), 30, 30, 30);
TopoDS_Shape fused;
BRepAlgoAPI_Fuse aFuse(b1, b2);
if (aFuse.IsDone())
{
  aFuse.SimplifyResult();
  fused = aFuse.Shape();
}