What is required for phone notifications to work?

I set up an automation to notify my phone when my wife’s phone entered a zone. If I run the automation manually, I get the notification. But the automation did not trigger on its own.

What are the requirements for that? Does HA have to be accessible from outside our wifi? For instance, do I have to have something like Nabu Kasa hookup so that HA works on internet?

Does the HA app have to be on the phone and connected?

Does phone location services have to be on for the phone?

What kind of battery usage does it cause?

Anything else?

Yes
Yes, or a dns service.
Yes
Yes
Not to much in my opinion. If I recall correctly I tested with screen on and high accuracy mode on with 5 seconds interval and it consumed about 10% battery during one hour.
I believe the screen was the thing that consumed the most to be honest.