What I am looking for is setting for:

when on profile's site, ......./view-persons-profile/xy-profile-name

there is a block named "Comments" related to that "xy-profile-name" where other members can write a comment to that profile (xy-profile-name)

Now, the Moderator and Admin can delete any of that comments on every profile (normal) but person with standard membership which actually created the profile can't. I think that the profile owner should be able to delete comments if he doesn't like the comment.