You should empty the stdin buffer before read something else.
void emptyBuffer() {
    char c="a";
    while (c != '\n' && c != EOF) {
        c = getchar();
    }
    return;
}
This function empty the stdin buffer.
    printf("Enter your name: ");
    scanf("%s", &string);
    emptyBuffer();
    fprintf(fw, "%d\n%s\n",p, string);
    printf("Enter your telephone number: ");
    scanf("%d",&cislo);
    emptyBuffer();
    fprintf(fw, "%d\n",cislo);
    printf("If u want to add more datas press Y otherwise press N ");
    c = getchar();
Because when you use getchar(), you probably get the last '\n' of the previous question (/answer).
And BTW (according to previous comments)
you should use: 
   if ( c == 'Y' || c == 'y' )
which is more user friendly 🙂
4
solved Yes/no does not work [closed]