If you really just want to know if the kid (or better, the ble tag) is at home, then no - I’d probably use any other ble beacon (iBeacons are cheap on Ali)
Afaik, Tile tags work somewhat like AirTags and are trackable wherever they are. If you want/need more precise location information then I’d stick to Tile.
Are you comfortable with flashing microcontrollers? https://esphome.io/components/bluetooth_proxy.html might be a solution to your BLE beacon idea. buy any esp32 board for like 5$, put it somewhere in your living room or wherever makes sense and have it proxy BLE scans to HomeAssistant.
I’m on Z2M, mostly because it supports more devices I’d like to use. If ZHA supports everything you have or might want to get in the future, I don’t see a reason to switch.
If you are the only one using the services, then go for a VPN instead of port forwarding or sth. This way, your stuff isn’t openly accessible from the internet to anyone poking around
+1. No idea what’s supposed to lead to this conclusion. I’d say that’s a bad PID tune.