Do I need to connect GPIO-O to the USB-Serial GND and the ESP GND to the ESP VDD?
GPIO 0 needs to be connected to GND (before VCC is connected) so ESP8266 goes into flash mode, and GPIO0 can be connected to GND during the entire flashing process. As for the other MCU, I’m not sure, @tbut7633 did say the other board was overheating and I don’t want to risk it. I desolder the 4 points between the two boards and separate the WiFi board (ESP8266) from the other MCU. This makes things simpler, you don’t need to worry about shutting it off.
Following step 5, will the device be able to power up and produce an SSID without reconnecting it back to the kettle power source?
After flashing, disconnect GPIO0 from GND, then disconnect and reconnect VCC. It should boot into your custom firmware (I use Tasmota) and you can configure it over wifi.
Which tools do you recommend to do the flash? I was looking at Tazmotizer.
I use esptool. Tazmotizer is a good choice too, it uses esptool under the hood.