1. Correct code to show CF7 in popup / iframe of fancybox:
<img src="/wp-content/uploads/2014/09/01-01.png" onmouseout="this.src='/wp-content/uploads/2014/09/01-01.png'" onmouseover="this.src='/wp-content/uploads/2014/09/01-02.png'"/>
<div style="display:none" class="fancybox-hidden">
<div id="contact_form_pop">
[your_contact_form7 shortcode]</div> </div>
2.To display another pop-up Contact Form 7 on the same page you need to add only 1 digit to a href="#contact_form_pop" and id="contact_form_pop".
See the code. I place 1:
<img src="/wp-content/uploads/2014/09/01-01.png" onmouseout="this.src='/wp-content/uploads/2014/09/01-01.png'" onmouseover="this.src='/wp-content/uploads/2014/09/01-02.png'"/>
<div style="display:none" class="fancybox-hidden">
<div id="contact_form_pop1">
[your_contact_form7 another shortcode]</div> </div>
3. To display more than 2 Contact Forms 7 on one page you have to add every time different digits.
4. One more example for newbies. Code for the 3rd Contact Form 7 on the same page where we placed code for 1st and 2nd pop-up CF 7.
<img src="/wp-content/uploads/2014/09/01-01.png" onmouseout="this.src='/wp-content/uploads/2014/09/01-01.png'" onmouseover="this.src='/wp-content/uploads/2014/09/01-02.png'"/>
<div style="display:none" class="fancybox-hidden">
<div id="contact_form_pop2">
[your_contact_form7 another shortcode]</div> </div>
5. I found this solution here - http://wordpress.org/support/topic/easy-fancybox-contact-form-7?replies=24
Many thanks to bgt9752!