This is most likely because of function overloading. When compiling with C, the call to fun(double) is translated into a call to the assembly function _fun, which will be linked in at a later stage. The actual definition also has the assembly name _fun, even though it takes an int instead of a double, and the linker will merrily use this when fun(double) is called.
C++ on the other hand mangles the assembly names, so you'll get something like _fun@int for fun(int) and _fun@double for fun(double), in order for overloading to work. The linker will see these have different names and spurt out an error that it can't find the definition for fun(double).
For your second question it is always a good idea to declare function prototypes, generally done in a header, especially if the function is used in multiple files. There should be a warning option for missing prototypes in your compiler, gcc uses -Wmissing-prototypes. Your code would be better if set up like
// file1.hpp
#ifndef FILE1_HPP
#define FILE1_HPP
void fun(int)
#endif
// file1.c
#include "file1.hpp"
...
// file2.c
#include "file1.hpp"
int main()
{
fun(5);
}
You'd then not have multiple conflicting prototypes in your program.