Question

extern int a;
int a = 1;

int main(void)
{
  return 0;
}

Is this UB? standard says in 6.2.2/7

If, within a translation unit, the same identifier appears with both internal and external
linkage, the behavior is undefined.

Answer 1

This is perfectly defined behavior. And this is what the compiler would get after pre-processing after an header is included.

Your confusion seems to come that:

int a = 1;

has not internal linkage. At file-scope a has external linkage. It would have internal linkage if the static specifier was added.