I want to edit the header.container block in order to add the social icons to the header page, unfortunately, I couldn't find the correct header.phtml file, would you please provide me furthur informations about this issue?
You can try enabling the path hints from admin. It will guide you to the path of the files that are rendering on the frontend. You can enable the path hints from
admin > system > configuration > select your store view from configuration scope > Advanced > developer > Debug > Template Path Hints
Set this option to yes & refresh frontend. It will show you all the path hints.
You can also enable Add Block Names to Hints to see which blocks are rendering.
Hope this will help you.