Yes you do need an internet connection to initially download ALL the charts, but after they are downloaded you should not need to do so again to use them as they are stored locally on your iPad 3G. In the second screen shot you show, only one of the charts for the region have been downloaded to iNavX. Once downloaded the chart names will appear in a bold font such as the third screen shot in my response above.
I also note you have your iPad in
"Airplane mode" which disables the internet connection and the iPad 3G GPS. As such it is impossible in this mode to download the charts or use them once downloaded. This is what is causing the error message in the second screen shot you have provided.
So I recommend you do this:
1) Turn "Airplane Mode" OFF in the iPad "Settings".
2) Enable "WiFi" connection
3) Return to iNavX and select any chart, when prompted, select "Yes, Download All..."
After the charts have downloaded you should not need to do so again.
Page 9 of this guide gives complete instructions for activating, downloading the charts from X-Traverse ..
http://www.fugawi.com/web/x-traverse/x-t...ctions.pdf