@Keyvanchan
We've had a battery camera for 4 years now, plugged in with no issues.
If you change Wi-Fi networks and are unable to set the network name and password on your new router/modem to the same values used on your old router/modem (that's what we did a couple of years ago), then you have to remove your cameras from the Google Home app (if you can), do a factory reset by pressing the factory reset button on the back of the cameras for at least 12 seconds until you get a solid yellow status light and a confirmation tone (this might take more than one try and longer than 12 seconds) (https://support.google.com/googlenest/answer/9252162), and then reinstall your cameras.
I'm not sure who is sending you emails, but you could try talking to a live person at Support:
1. Go to https://support.google.com/googlenest/gethelp.
2. Select a category/product family, and type in a brief description of the issue, then click "Next".
3. Select your device from the dropdown, click "Other", then click "Next step".
4. Under "Resources", just click "Next step". (Clicking one of the listed links will bring up a Help page.)
5. Under "Contact options", choose to get a phone call or chat with the team, depending on availability in your country.
