Sorry I didn't see this on the 19th when you posted it!
Looking at your template, one thing I see is that your command is:
SubmitToSharePointList /submit=TestSubmit /mapping=mapping /id=my:id
But in your data source the ID field is "ID". This would mean your command should be (bold for emphasis):
SubmitToSharePointList /submit=TestSubmit /mapping=mapping /id=my:ID
To see what your error might be from the qRules submit, you can put the QdabraRules error node on your form, so that after you run the command, you can see if there are any errors. I've attached a copy of the form template with these changes, so that you can try previewing it again and see if any errors are recorded to the errors node. Right click the link in the post header, Save As to save locally, right click the saved file and select Design to open in design mode.
So you know, I have not had to make forms full trust to run this command. Also, on my machine, I was able to preview the form without it being full trust. What errors were you getting on preview?