mohsh86:
I am using Software Serial 19200 baud rate (which isn't max), the problem is:Pro Mini Tx -> ESP8266 Rx is fine, sending always and receiving correctly
ESP8266 Tx-> Pro Mini Rx is not stable, i got one clear message every random sends
My experience is that Software Serial works stable only up to 9600 baud (sending may be ok with higher rates, but receiving is not). You can try AltSoftSerial.
both are powered separately through different USB ports
This might not be a very good idea, if GND and GND AND Vcc1 and Vcc2 from the two USBs are connected somehow. But to tell more, a schematic wold be necessary.