Well, this is dull men's club, and that isn't very dull. But if you insist, lightning struck and the power surge destroyed my doorbell. Luckily and strangely, that was the only thing damaged.

It also gave me an excuse to buy a cool new doorbell. I'm not made of money, but I certainly can't go without a doorbell right? And certainly, I only bought this one because it uses PoE and my PoE is already behind surge protection so the same thing can't happen again. It had nothing to do with how cool this doorbell is, and everything to do with safety, of course.

I'm not 100% sure, but I believe they can. Recordings are all local, pattern recognition is local, users are local, etc. I have never tried to cut it off from the internet completely because I want to use the doorbell while I'm away, but I don't see why it couldn't be. They do have frequent software updates though which need internet to install.

I have a local UNVR that stores my recordings and runs the unifi protect app that controls all of my cameras.

Local recording is in fact currently the only option, you're forced to buy one of their assorted NVR devices to use Ubiquiti's cameras.

(Technically it could be in another location streaming from the camera to the NVR across the internet, but you're still obliged to control both ends of that equation)

You can optionally have remote access either through Ubiquiti (which judging by the question I'm assuming you would not want) or by your own VPN or other self-controlled method.

There's also good integration with Home Assistant, which you can use for notifications based on motion detection or other events. I use that method for my doorbell, playing an mp3 out of one of the speakers in the house, due to the lack of any actual doorbell chime. They'll also sell you a PoE-powered chime that links to the NVR though.

This might also work for the normal g4, the ssh instructions might apply.