esp8266 not getting programmed
Be careful, you could fry your ESP like that.  You need to get the signal lines down to 3.3V, not the 5V used by the Arduino Uno.  There are many ways to do this, from voltage dividers, to transistors, or you can use a 3.3v Arduino Pro Micro.  I would also recommend starting out with just a 3.3v FTDI board, and interface that directly to the ESP to remove the Arduino and its code from the picture.  

I would also make sure that your grounds on the external supply and the Arduino are tied together, or just power the ESP from the 3.3v out of the Arduino.  

Other than that, double check your baud rate, some come shipped at 9600, some at 115200, and i'm sure that there are others out there too shipping at different baud rates.