Are my comments and mentions hidden?
If someone with a private profile mentions someone who isn't one of their approved followers on a photo or video, the person mentioned will be able to see part of the comment in the You section of Activity. They may get a push notification (if their notification settings are turned on), but won't be able to navigate through to the private photo or video.
If someone with a private profile leaves a comment on a photo that a public Instagrammer uploaded, their comment will be visible and their username will be clickable below that photo.
If you send a photo/video to a specific group of people with Instagram Direct, only those people can see the comments or mentions associated with that photo/video.