So far i worked with ESP8266-01 and ESP-12F none of them has a regulator on it. I always provide 3.3V. Can you be more specific about ESP8266 ? are you using NODEMCU or something else ?
I had thought that the two side-by-side pads used for the output voltage were actually identical/redundant and just provided for convenience.
For question 1 and 2 i suggest you to use schottky diode to isolate two different power sources from each other. You will not concern about for the cases 1 and 2.
Excuse my ignorance of electronics .. would that be like using some regular rectifier diode? And would there not be a voltage drop created by the diode? Where would I place it / them?