Terrain Terrain
Bitburger
E-GPWS accounts for terrain from a database: TAWS altitudes are based on "real" altitudes, feet from sea level. All corrections to altimeters, pressure and temperature related, have to be applied by the pilot(s).
As far as the people are concerned who write about the radar altimeter looking straight down - yes, that is valid for old fashioned GPWS. E-GPWS on the other hand works with a GPS receiver that supplies position, a database that supplies terrain around position and hence a warning system that can supply look-ahead warning of terrain.
Whether man made structures are included in the database - simply said, that depends on the database - consult your company's instructions for the latest truth in that matter (yes, the truth changes every day).
Edit: added third paragraph as an afterthought.