The answer to your original question
How to read a string one char at the time, and stop when you reach end of line?
is, in C++, very simply, namely: use getline. The link shows a simple example:
#include <iostream>
#include <string>
int main () {
std::string name;
std::cout << "Please, enter your full name: ";
std::getline (std::cin,name);
std::cout << "Hello, " << name << "!\n";
return 0;
}
Do you really want to do this in C? I wouldn't! The thing is, in C, you have to allocate the memory in which to place the characters you read in? How many characters? You don't know ahead of time. If you allocate too few characters, you will have to allocate a new buffer every time to realize you reading more characters than you made room for. If you over-allocate, you are wasting space.
C is a language for low-level programming. If you are new to programming and writing simple applications for reading files line-by-line, just use C++. It does all that memory allocation for you.
Your later questions regarding "\0" and end-of-lines in general were answered by others and do apply to C as well as C++. But if you are using C, please remember that it's not just the end-of-line that matters, but memory allocation as well. And you will have to be careful not to overrun your buffer.