Apologies in advance for the lengthy post, but I am writing as I look through.
1. I note that there is a captcha element mentioned in the SQL and have found a couple of oddities on the captcha element:
1a. There is a blank tab on the Details page before "Standard captcha options" - this could be a bug or a bad install of Fabrik. On my site this tab is called "Options" - which suggests that there is an install issue with the Captcha element plugin - but I cannot diagnose this without superadmin access and / or access to the web server directories.
1b. The captcha element is published and set to "show in list" - not sure that "show in list" makes any sense, but it doesn't appear in either form or list, perhaps because it has not been fully configured. I have unpublished this element but this didn't help.
2. I tried using fabrikdebug=1 on the form, however it looks like fabrik debug is not enabled in fabrik options. Not being superadmin, I cannot turn this on myself. I recommend during dev that you turn this on and turn on maximum php reporting in Joomla Global Settings also.
3. I noted that two elements (id and date_time) were not associated with a group / list / table - and I think that it is the lack of id which is the problem. In the list you do not have a primary key set, and there are no elements in the list. Essentially Fabrik needs a primary key for every List.
4. However when I tried to re-enable the id field, the element would not save. Looking into the HTML for an element edit and comparing it to my own site, there are key parts of the HTML missing and some odd empty divs with weird names inbetween </head> and <body>. Definitely something weird here.
However the symptoms are similar to a problem reported and fixed in March (see
http://fabrikar.com/forums/index.php?threads/save-other-buttons-stop-working-for-an-element.32711/ ). Since you say that you have updated from GitHub recently, I think that there may be a basic issue of how Fabrik is installed or your GitHub updates are not working.
SO.....
A. I suggest you re-update from GitHub carefully following the instructions in the wiki and see if that helps. If it does, then...
B. Re-enable the "id" field as every record needs a primary key (and this is probably the cause of the SQL error above).
You may also want to re-enable the date_time field as I would imagine it would be useful to know the date and time that the contact record was saved.
Hope this all helps.
S