char two_character_string[2];
//You cant do this outside a function!
two_character_string[1] = '\0';
two_character_string[0] = c;
It should be this:
char two_character_string[2] = "c";
or this:
char two_character_string[2] = {'c',0};
or this:
char two_character_string[2] = {'c','\0'};