Esp8266 communication with arduino

void loop() {
if(client_checker()); //Serial.println("connection available");
}

Why is the call to client_checker() wrapped in a useless if statement?

Why does loop() do nothing more than call one other function?

 success&=send_command(restart);

Isyourspacekeybroken?

    if(a[0]=='S' && a[1]=='E' && a[2]=='N' && a[3]=='D' && a[5]=='O' && a[6]=='K') answer=13;

Are you serious? Get real. Learn to use memcmp().

  for (byte i = 0; i < input_buffer && Serial.available(); i++) {
   
    c = Serial.read();
    digitalWrite(ledPin,!digitalRead(ledPin));
    a[i] = c;

This will spin through this loop VERY quickly, splattering data all over the a array (what a stupid name).

It will NOT fill the a array in order.

    c=(receive_command());

(Why) (is) (the) (call) (wrapped) (in) (useless) (parentheses) (?)

I gave up trying to understand the code, with the useless names for the variables.