If you use compact menu even on desktop, you can add this function in your functions.php file:
function brand_compact_navigation() {
$brand_settings = wp_parse_args(
get_option( 'brand_settings', array() ),
brand_get_defaults()
);
$search_icon = 'enabled' === $brand_settings['nav_search'] ? '<a href="#" class="search-form-icon"><i class="fa fa-fw fa-search menu-search-form-icon"></i></a>' : '';
?>
<div class="compact-menu-icons">
<?php echo $search_icon; // WPCS: XSS ok. ?>
<ul style="list-style-type:none;margin:0 10px;padding:0;"><?php pll_the_languages( array( 'show_flags' => 1, 'show_names' => 0, 'hide_current' => 1 ) );?></ul>
<a id="mobile-menu-button" class="c-hamburger c-hamburger--htx">
<span>toggle menu</span>
</a>
</div>
<?php
}
Adjust pll_the_languages function as you need, you can find more in the documentation.
I suggest to use a child theme, or you’ll lost your changes on next theme update.
To show the logo on mobile devices you have to choose an image in Site Identity > Mobile logo.