Under Facebook’s Page settings, you can control whether the public can:

Facebook Page settings offer comprehensive control over public interaction. You can manage whether others can tag photos you've posted to your Page, preventing unwanted associations or spam. You also have the ability to restrict or allow visitors to post directly to your Page's timeline, which is crucial for maintaining content quality and brand image. Furthermore, Page settings allow you to enable or disable private messaging, determining if people can contact your Page directly through Messenger. Therefore, all these options are controllable within Facebook's Page settings.