Does this work without an internet connection (once downloaded)? If yes, How big is the downloaded footprint? I still haven't gone through the webpage carefully.
If you use Sphinx for speech recognition and use pyttsx for text to speech (Windows Speech API, OSX NSSS, or ESpeak on Linux) it all works offline - see the "Jarvis's Brain" section.
No, except for the stt part using sphinx, which is tricky to set up for it to be accurate enough (seems the author of the op didn't go that far)