Yes, the admin can set the conditions like show the label only for products which attribute set is Bag or category is Gear. Reference guide: https://magediary.com/docs/product-labels#product-conditions
Yes, set the Enable for Product View and Enable for List View fields accordingly under the Permissions tab. Reference guide: https://magediary.com/docs/product-inquiry-support.html#permissions
The guest user gets the View Inquiry link in the email that they get on submitting the reply by the admin. By clicking on the view inquiry link, the user can view and submit a new reply from their end. Reference ...