Construction and destruction of Geometries is done using geos::geom::GeometryFactory.
You'll feed it geos::geom::CoordinateSequence for base geometries or vectors of geometries for collections.
If you need to construct geometric shaped geometries, you can use geos::geom::GeometricShapeFactory.
GEOS version info (as a string) can be obtained using geos::geom::geosversion(). The JTS version this release has been ported from is available throu geos::geom::jtsport().
For WKB input/output you can use geos::io::WKBReader and geos::io::WKBWriter
Note that prior to version 3.0.0, GEOSException were thrown by pointer, and did not derive from std::exception.