1. The doorbell cam is connected only to the LAN.
2. The doorbell cam is definitely blocked from accessing the internet.
3. Having access to the LAN from your phone through VPN allows you to watch the feed and talk to people at the door through the app.
2. I have not gone through the trouble of isolating them on their own VLAN, but I don't see any traffic coming from the devices. This is something you will want to audit on your own network if it is important to you.
3. I have viewed the camera output through VPN, but have not yet tried speaking through the doorbell (or through one of my camera's audio output). I don't see why it would not work.
The Reolink doorbell camera is a typical recommendation and can work fully locally and supports well the common standards like RTSP. 2 way audio works as well.
I believe the NVR Reolink sells can also work fully locally as well. Which also can integrate to home assistant.