Serial.begin on ESP8266 not working
There are two options left for you to try based on all the information contained on this thread.
1. Fix the connections as follows:
You need to connect a few GPIO pins on the ESP-12 to 3.3V or Ground, to set it in the right mode for communicating with it. You can add capacitors and resistors where you feel they may be needed, however the AI modules have those internally already. In addition, remember to remove this setup when resetting the board to run your firmware, otherwise it will be booted into &quot;Programming/Flashing Mode&quot; which can have undesirable effects. Please note that this diagram uses a LM1117 voltage regulator, if you have a 3.3v power supply you can just substitute that in the diagram. Here are the connections you need to make:

ESP-12 &lt;--------&gt; TTL-USB
TX  ----&gt; RX
RX  ----&gt; TX
GND ----&gt; GND
REST ----&gt; RST (only if you plan on using the serial console to reset the board.)
ESP-12 &lt;--------&gt; POWER SUPPLY
VCC ----&gt; 3.3V Power supply (Vout of Voltage Regulator or Power Supply)
GND ----&gt; Ground of power supply
CH_PD ----&gt; HIGH (3.3V)
GPIO2 ----&gt; HIGH (3.3V)
GPIO15 ----&gt; LOW (GND)
GPIO0 ----&gt; HIGH or Floating for AT Mode (3.3V) [ * if you want to flash
completely different firmware then you must connect it to ground ] It appears you
have this connected to HIGH which is why you may be having problems flashing
Arduino Sketches.
2. Reflash the AT firmware using ESPTOOL
If you are still having problems after the reconfiguration of your connections, I highly recommend that you reflash the AT firmware from Espressif and start from scratch. If this doesn't fix your problem then I am afraid you have fried your board.
(For more detailed instructions see Instructables)