Hey Alexander,
If you want a search bar inside the mobile menu, add this in the functions.php file:

add_filter( 'wp_nav_menu_items', 'avf_add_search', 3, 2 );
function avf_add_search( $items, $args ) {
	if ($args->theme_location == 'avia')
	{
		$search = '<li id="menu-item-search-mobile" class="menu-item menu-item-type-post_type menu-item-object-page current-menu-item page_item page-item-18 current_page_item menu-item-top-level menu-item-top-level-5">'.get_search_form(false).'</li>';
		$items = $search . $items;
	}
	return $items;
}

After that, use this code in the Quick CSS field:

@media only screen and (max-width: 767px) {
	#top #searchform>div {
		display: block !important;
		opacity: 1 !important;	
	}
}

Best regards,
Mike