You want to use single quotes:
if(c=='\0')
Double quotes (") are for strings, which are sequences of characters. Single quotes (') are for individual characters.
However, the end-of-line is represented by the newline character, which is '\n'.
Note that in both cases, the backslash is not part of the character, but just a way you represent special characters. Using backslashes you can represent various unprintable characters and also characters which would otherwise confuse the compiler.