The problem you show in the last image is caused by fitting a skin surface to an area that has too much change in curvature. The solution is to skin smaller areas and have more faces in the surface.
I can’t comment on meshing problems with ICEM because I don’t use that software. When I use Ansys Mesh, there is no problem meshing the air around the solid filled wing.
What output options are available to change the quality of the STL output from your unnamed softare? For example, here are the options for SpaceClaim. Notice in the Resolution section the controls over how closely the STL follows the underlying geometry that it is approximating with facets.
I found the sharp edges in the top side near the trailing edge. I see the sharp edge at the top of the peak, and a less sharp edge on the left just before the edge of the wing. Is that less sharp edge important or is it supposed to be smooth and you have an artifact in the STL representation of the real geometry in the unnamed software?
Here is a close up part of that peak:
I made 3 faces using the Skin Surface tool. Notice that the top peak remains sharp, but the less sharp edge to the left of the peak has been smoothed, even though there is a face boundary.
Is that less sharp edge to the left of the peak important or is it supposed to be smooth and you have an artifact in the STL representation of the real geometry in the unnamed software?