Adding Information to right of header

Enfold Theme Options -> header layout -> extra elements

does that help?

depending on how good you’re with coding,the logo is added at line 438 in enfold\framework\php\function-set-avia-frontend.php

$logo = "<$headline_type class='logo'><a href='".$link."'>".$logo."$sub</a></$headline_type>";

something like:

$logo = "<$headline_type class='logo'><a href='".$link."'>".$logo."$sub</a><div style=\"float:right;\">my text</div></$headline_type>";

!!!but i would wait for the real support because i dont like my own solution and it might get overwritten with an enfold update!!!

inside the custom.css in your enfold theme there is a extra section for the mobile css.

Or you use this in quick css:

@media only screen and (max-width: 767px) {
#advanced_menu_toggle {
your css
}
}

you can give the div from my previous answer a class or id to target it easier.
A link to your site would also help to see how it looks.