Serial.println doesn't output correctly

Projects Programming
1

That's a program to take input from user and then test the string if it's palindrome or not .
the program runs fine with the led but why i can't output

Serial.println((String)s[i] +(String)" == "+(String)s[sz-i-1]);

it dousn't output anything and before this print , I tried the one with message "got here" but every time it lacks a letter like this
ot here
t here
here ....

that's my code

bool done = false;
String s ;
void setup() {
  Serial.begin(9600);
  pinMode(13, OUTPUT);
  digitalWrite(13, HIGH );
  s = "";
}
bool isPalindrome() {
  int sz = s.length();
  delay(1000);
  /*Serial.println("got here " + sz);
  delay(1000);*/
  for (int i = 0 ; i < sz / 2 ; i++) {
    delay(500);
    Serial.println((String)s[i] +(String)" == "+(String)s[sz-i-1]);
    if (s[i] != s[sz - i - 1]) {
      return false ;
    }
  }
  return true;
}
void loop() {
  if (done) {
    if (isPalindrome())digitalWrite(13, HIGH);
    else digitalWrite(13, LOW);
    done = false ;
  }
}
void serialEvent() {
  while (Serial.available()) {
    char c = (char)Serial.read();
    if (c == '\n')done = true;
    else {
      s += c;
      //Serial.println(s);
    }
  }
}
2

don't over-use the String class... just do

Serial.print(s[i]);
Serial.print(" == "); 
Serial.println(s[sz-i-1]);

I would suggest to study Serial Input Basics to handle getting the input from the user... Don't use the String class.

3 
Serial.println("got here " + sz);

That is equivalent to:

char foo[] = "got here ";
Serial.println(&foo[sz]);

As 'sz' counts up you are starting further and further into the string.

What you should have written is:

Serial.print("got here ");
Serial.println(sz);
4

You forgot to clear out 's' after you check it. Further input characters get appended to 's'.