Configuration > Advanced > Data integrity checks the database of your site for two kinds of problems:
The check runs when you open the page. It only reads your data. Nothing is deleted until you click one of the red buttons.
When the consistency check finds problems, it lists them and asks Should we proceed with the delete? Click Yes, delete them! (1) to remove the broken entries. Then open the page again: some problems only show up after the first fix.
In the picture: 1 Yes, delete them! removes the entries the consistency check lists, 2 the old response tables and participant lists, 3 Delete checked items!
When you deactivate a survey, LimeSurvey keeps its responses and participant list in old tables, listed with the survey ID, the date and the number of records.
Note: You cannot undo this. The old tables are the only copy of those responses unless you exported them. See Recover responses after deactivation.
Yes. Opening it only runs the check. Data is deleted only when you click Yes, delete them! or Delete checked items!
Only when you are sure you won't need those responses again. Export them first if in doubt.