Hi Pasha!
We have a detailed guide describing how you can migrate the staging site to the live site for free, it’s published here. Due to the fact that every website has its own setup and server configuration, the guide describes the general basic steps that suit most sites, but we can’t provide support for this guide per specific site.
The free version doesn’t have the option to push the staging site to the live site, that’s clearly stated in the plugin’s description here, however, it allows you to get a cloned copy of your live site to test new theme, plugin or even a new WordPress version away from your live site, you can also use it to create a backup of your site and restore it anytime if something goes wrong.
I would love to see the email conversation you pointed to, but it’s not appearing, please send a screenshot of it via this form and mention this forum thread.
Thanks,
Alaa