In actuality, I removed the register and login divs from the .ascx file (namely Home-Standard-Menu.ascx).

So with the space clear, I would like to get the Social Media icons with the language icons on the same line instead of Language on top of Social Media...

Can this be done in the existing installation?

Thank you

Sure.

You can edit the skin and insert the icons as part of the skin.

Alternatively, you can insert a content page where you removed the skin objects. You can then put anything you like there. That could be an HTML module with social icons in the content. Set the module to appear on all pages.