With links on Images i meant actually two things: The image urls and the Links around the images
<img src=??? .../>
But on your page is obviously nothing.
The Rest seems to Work as you can see http://alternateroute.com.au/gallery3/index.php/rest/item/1?output=html
I could reproduce your error in my Testsite. Getting the Members at wpg3_class_WPG3_Xhttp.php line 163 don't work. This request returns just '' but it should retun the members as described in http://codex.gallery2.org/Gallery3:API:REST#Items
Which Version of Gallery3 are you using?