ESP8266 Send data to Firebase using Arduino Uno error
1.) Can I input/flash code in my module using my arduino and adapter?


Yes


  2.) Since the button is plugged in the pin 8 of arduino. Does that mean If the code in the module will be successfully inserted. I will still need the arduino to be plugged in the buttons?


The ESP8266 cannot magically know about the Arduino and the Arduino cannot magically know about the buttons. If you have buttons connected to the Arduino then the Arduino needs telling about them. If the Arduino and ESP8266 need to work together then they both need programming to work together. If, and only if, you connect the buttons to the ESP8266 and not the Arduino do you not need the Arduino.


  3.) What could be the reason why the module won't appear in the Port List and generates the errors?


The Arduino is getting in the way. Connect Arduino RESET to Arduino GND to disable the ATMega328p chip which is also trying to use TX and RX and conflicting with the ESP8266. Or better still get a cheap USB to UART cable (just a couple of dollars on eBay) and connect the adaptor direct to your PC without the Arduino.