Compile with VS2017

This is fixed. I can compile with VS2019.

Regarding the definition of GEOSGeom, my environment is finding it in <ogr_geometry.h>
Regarding the definition of wkbNone, my environment is finding it in <ogr_core.h> (which is what you specified)
Regarding the definition of CString, my environment is finding it in <afxstr.h>
Regarding the ambiguous definition of HRESULT in Shapefile.h, does it tell you where the multiple definitions are coming from? My environment is finding the definition in winnt.h

My hunch would be to add the GDAL include file <ogr_geometry.h> to GeosConverter.h (instead of adding <geos_c.h>)
Then adding the GDAL <ogr_core.h> to GeosConverter.cpp

I'm not sure of the difference between afxstr.h and atlstr.h, I will have to review that.
EDIT: I believe that afxstr.h is associated with MFC, while atlstr.h is associated with ATL. Moreso, it appears that atlstr.h includes a generic definition of a CStringT class, and defines a more specific CAtlString class. Based on this, I believe it would be more appropriate to include afxstr.h since we are generally using CStrings rather than CAtlStrings.

At some point, I should get a clean download of the source and build it from scratch...

I have a new laptop with only VS2017 installed.
When I rebuild the Debug|Win32 solution I get these errors:

GeosConverter.h

Solved by adding #include <geos_c.h>

GeosConverter.cpp

Solved by adding #include <ogr_core.h> and #include <ogr_geometry.h>

Solved by adding #include <atlstr.h>

Shapefile.h
This file has a lot of errors about

And a lot of errors about the used macros.
Not sure how to fix these.
Adding #include <geos_c.h> and #include <ogr_api.h> solve some other errors.

It looks to me something is not correctly configured.
I'll wait for and his suggestions.