Yes, PGE needs an active Internet connection because it accesses Google Maps.
You can't set a proxy server in PGE: the software uses the same proxy settings as your Microsoft Internet Explorer.
Photo GPS Extract is freeware and will always remain so. You are allowed to use the program in corporate environments.
Adding GPS data is done during a process called 'Geotagging'. I wrote a small article on geotagging with more information.
I deliberately decided NOT to build a geotagging feature. The design philosophy of Photo GPS Extract has always been the same: the software does NOT alter your photos in any ways.
Starting from PGE 7 there is an option to write some Exifdata with an external tool called 'ExifTool'. This is a reputed software uses by many people around the world. The external tool is configured in a way that it always creates a backup of your original photo.