Receiving serial data as string and comparing them with other strings

A null-terminated char array is often called a string, a String is a C++ class.

== won't work with an array of char, use strcmp() or make char_in a String (not the preferred option on a small chip like the Arduino).

Also you have to terminate char_in with a '\0'.

    char_in[i++] = Serial.read();
      char_in[i] = '\0';

Rob