Trying to communicate with an ESP8266

Unless you have some project constraints which make it mandatory to use naked ESP8266, why not use a NodeMCU to communicate with the Arduino in a master/slave relation over I2C?

#include <Wire.h>  
#define I2CAddressESPWifi 8

in setup()

Wire.begin(D1,D2); // SCL D1 SDA D2

then call from anywhere inside your loop() call this function

char readSlave(int x) { // send current time
  String xY = String(x);
  char c;
  int charArrayLength = xY.length()+1;
  char bufferChar[charArrayLength];
  Wire.beginTransmission(8);
  xY.toCharArray(bufferChar, charArrayLength);
  Wire.write(bufferChar);
  Wire.endTransmission();
  delay(10);
  Serial.print("wire sent: [");
  Serial.print(x);
  delay(50);//Wait for Slave to calculate response.
  int counter = 0;
  char buffMe[32];
  int bytesIn = Wire.requestFrom(8,32);
  while (Wire.available()) {
    delay(2);
    buffMe[counter] = Wire.read();
    /*
    c = Wire.read();
    Serial.print(c);
    */
    counter++;
  }
  delay(10);
  Wire.endTransmission(); 
  delay(500);
  Serial.print("] bytesIn: [");
  Serial.print(bytesIn);
  Serial.print("] buffMe: [");
  Serial.print(buffMe);
  Serial.print("]");
  return buffMe;
}

and your arduino will be waiting (setup)

Serial.begin(9600);
// slave listens for call from master NodeMCU
Wire.begin(I2CAddressESPWifi);  // predefined as `8` or whatever address you choose
Wire.onReceive(receiveEvent);
Wire.onRequest(requestEvent);

and at the end of your code

void receiveEvent(int howMany) {
  if (howMany) {
    Serial.print("bytes[");
    Serial.print(howMany);
    Serial.print("] Received[");
    char charIn[howMany];
    int counter = 0;
    while (Wire.available()) {
      char c = Wire.read();
      charIn[counter] = c;
      //Serial.print(c);
      counter++;
    }
    delay(10);
    //do something with command from master
  }
}
void requestEvent() {
  char bufferChar[20] = "slave answer string";  // automatically null terminated extra character at end
  Serial.println(bufferChar);
  Wire.write(bufferChar);
}