Power Arduino Mega ESP85266
Is it possible to Power a Arduino Mega 2560 and a NodeMCU V2 ESP8266 ESP-12E from a single 9V Block?


Yes. Assuming the "block" can provide enough current.


  Can i power the ESP8266 directly via the Arduino Mega 5V output? (3.3V Output seems to weak)


No.


  Is a Power Converter like this for the ESP8266 necessary?


Yes if you are powering it from more than 3.3V.


  Should I use another external Power source for the ESP8266?


Not necessary if the 9V one can provide enough current as I mentioned above.