I use Google Sheets in a similar way on some of my Tableau Public vizzes, some of them that are populated from Google Forms (not Jot Forms)
About your questions:
1- I am not sure what is the "Clean data" option you refer to (Is that about using Data Interpreter?). Anyway I believe that the data interpreter will re-run on each refresh so that the data keeps the same shape you used to build the viz. You may need to test some scenarios to check if it will break or not the viz on Tableau Public.
2- Tableau only reads the data from the sources so I don't believe it will break the integration. Maybe you need to contact Jot Form support to check what happened?
Let me know if these helps.
Were you ever able to determine the best way to connect Tableau to your Jotform data? If so, would you mind sharing?