Any circle type can have an Outer Circle.
People in an Outer Circle will only be able to see certain entries, specifically, the ones that have checked the "Include outer circle" box.
As with ALL circle members, if you set the Priority to "urgent", it will send the note to everyone according to their Do Not Disturb and Delivery Method preferences.
Emergency notifications should be used only in dire circumstances. An emergency notification will be sent immediately to everyone using every Delivery Method they have provided, regardless of their Do Not Disturb preferences. With this in mind, if you really really cannot be disturbed, even in an emergency, then you may want to consider muting or turning off your phone.