extern "C" causing an error "expected '(' before string constant" [duplicate]

Question

file1.c

int add(int a, int b)
{
  return (a+b);
}

file2.cpp

void main()
{
    int c;

    c = add(1,2);
}

h1.h

extern "C"  {

#include "stdio.h"

int add(int a,int b);
}

Case 1: when i include h1.h in file1.c file then gcc compiler throw an error "expected '(' before string constant".

case 2: when I include h1.h in file2.cpp file compilation work successfully

Question:

1) Does it mean that I can not include header file in C with extern "C" function in it??

2) Can I include header within extern"C" like shown below

extern "C" {

#include "abc.h"
#include "...h"
}

3) Can I put c++ functions definitions in header file with extern "C" so that i can call it in C file?

for example

a.cpp ( cpp file)

void test()
{
   std::printf("this is a test function");
}

a.h (header file)

extern "C" {
void test();
}

b_c.c ( c file)

#include "a.h"

void main()
{
  test();
}

Answer 1

Write a.h like this:

#pragma once
#ifdef __cplusplus
extern "C"
{
#endif

int add(int a,int b);

#ifdef __cplusplus
}
#endif

This way you can declare multiple functions - there is no need to prefix each one with extern C. As others mentioned: extern C is a C++ thing, so it needs to "disappear" when seen by C compiler.