Notifications away from home

Hi there A question about when I’m away from home. Other than video doorbell alerts and assisted monitoring calls when the alarm is triggered, will I get notifications on my phone when there is some sort of activity in my house? So for example if I’m away from home and the alarm is triggered can I get a push notification on my phone as well as a call? Or if I forget to set the alarm for any reason when going out, would I get a notification if there is some sort of activity such as a motion sensor detecting movement? Or does my phone need to be connected to the same WiFi as other ring devices? Many thanks!