Hello,

1-Please add this code into your Custom Css box:

@media (max-width: 480px) {
.extra_tools_wrapper .tool.account {
    display: block !important;
}}

2-Please add this code:

@media (max-width: 480px) {
input.search-field.input-search-field {
    margin-left: -99px !important;
}
.extra_tools_wrapper.style-small .tool {
    width: 22px !important;
}}

This should be the result: https://postimg.cc/image/hzwnvgeif/
3-As for the search text appearing in search icon, please go to file \includes\codeless_builder\header-elements\cl_header_search.php
find this line:
<input type="search" id="<?php echo esc_attr( $unique_id ); ?>" class="search-field input-search-field" <?php $this->generateStyle( '.search-element .input-search-field', true ); ?> placeholder="<?php echo esc_attr__( 'Search Your Style', 'june' ); ?>" autocomplete="off" value="<?php echo get_search_query(); ?>" name="s" />
Edit to this:
<input type="search" id="<?php echo esc_attr( $unique_id ); ?>" class="search-field input-search-field" <?php $this->generateStyle( '.search-element .input-search-field', true ); ?> placeholder="<?php echo esc_attr__( 'Search Your Style', 'june' ); ?>" autocomplete="off" value="" name="s" />
Save changes.
Let us know.

Best regards!

Hello,

1-Changing the search style to this one, requires more coding than the above. Sorry but this is a customization not included in support.

2-For menu display in the iphone 5 screen, please add this code:

@media (max-width: 340px){
.extra_tools_wrapper {
    display: block !important;
    visibility: visible !important;
}}

Best regards!