converting int or byte to ascii

surepic:
couldn't describe the whole schematic too much to write decide to upload image.

OK... that not how I wired up my arduino. this is your code that I ran (getting same issue as u)

#include <SoftwareSerial.h>

SoftwareSerial mySerial(10, 11); // RX, TX
//char string[] = "AT\r\n";
void setup() {
  // Open serial communications and wait for port to open:
  Serial.begin(115200);
  while (!Serial) {
    ; // wait for serial port to connect. Needed for native USB port only
  }
  mySerial.begin(115200);
  Serial.println("arduino");
  mySerial.println("AT");
  //delay(100);
  //mySerial.write("AT");
  Serial.println("Esp");
}

void loop() { // run over and over
  while (mySerial.available()) {
    Serial.write(mySerial.read());
  }
}

your schematic does not really tell but how did you manage to print "mySerial.println("AT")" and "Serial.println("Esp")" to the SAME serial monitor when u tested the code? did you wire things differently then?