The concept behind Profiling Surveys is to update profile information over time. Instead of doing a huge profile model, you can add profile fields in the profiling survey category and "backfill" them over time.
Communities >> Profile >> Add New Profiling Surveys
When adding a Profiling Survey for the first time, you can set the Status for the survey as Draft/Hidden. The survey will not show up on the Panel. Once you have finalized the survey, set the Status as Active to make the survey live.
Profiling Surveys are similar to surveys (from the end-user's standpoint) - and will be displayed in the My Surveys section.
Yes, completed Profiling Surveys will appear in the My Profile section and members can then update their Profiling Surveys.