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I would recommend using multidemnsional arrays for both your contacts and your light states.

//------------------------------------------------ declare variables

char* titles[] = {"RELATION", "FIRST NAME", "LAST NAME", "LOCATION", "PHONE NUMBER"};

char* econs[][5] = {
  {"SELF", "JOHN", "SMITH", "FLORIDA", "999-888-6666"},
  {"BROTHER", "MICHAEL", "SMITH", "FLORIDA", "999-888-5555"},
  {"WIFE", "EMILY", "SMITH", "FLORIDA", "999-888-4444"},
  {"SISTER", "SOPHIA", "ADAMS", "NEW YORK", "888-777-3333"}
};

uint8_t lights[][4] {   {HIGH, LOW, LOW, LOW},
  {LOW, HIGH, LOW, LOW},
  {LOW, LOW, HIGH, LOW},
  {LOW, LOW, LOW, HIGH},
};

int ledPinOne = 2;
int ledPinTwo = 3;
int ledPinThree = 4;
int ledPinFour = 5;
int buttonPin = 6;
int state = 0;

//------------------------------------------------ setup - set pins
void setup() {
  Serial.begin(9600);

  pinMode(ledPinOne, OUTPUT);
  pinMode(ledPinTwo, OUTPUT);
  pinMode(ledPinThree, OUTPUT);
  pinMode(ledPinFour, OUTPUT);
  pinMode(buttonPin, INPUT);

  Serial.println("Emergency Contact");
}

//------------------------------------------------ main
void loop() {


  if (digitalRead(buttonPin))
  {
    if (state > 3)
      state = 0;
    
    {
      for (int y = 0; y <= 4; y++)
      {
        Serial.println(" ");
        Serial.print(titles[y]);
        Serial.print(" ");
        Serial.print(econs[state][y]);
      }

      Serial.println(" ");
      setLights(lights[state][0], lights[state][1], lights[state][2], lights[state][3]);
    }

    delay(1000);
    state++;

  }

}


//------------------------------------------------ function to turn LEDs on/off

void setLights(int one, int two, int three, int four)
{
  digitalWrite(ledPinOne, one);
  digitalWrite(ledPinTwo, two);
  digitalWrite(ledPinThree, three);
  digitalWrite(ledPinFour, four);
}

I haven't tested the above, but it should provide the same result.

As for the second part of your question, there is an autoformat tool in the Tools menu that will auto-indent your code. Ctrl-T will do the same.