must have been very urgent ;)

i do not see private content – because i’m participant as you.

But on that topic only one button row is used – i changed code to a nested each function ( with nice use of this ;) )

function id_to_button_row_buttons(){
?>
<script>
(function($) {
	$('.avia-buttonrow-wrap').each(function(){
		var that = this;
		$('.avia-button', this).each(function(i){
			var ButtonRowID = $(that).attr('id');
			$(this).attr('id', ButtonRowID+'-button'+(i+1));
		});
	});
})(jQuery);
</script>
<?php
}
add_action( 'wp_footer', 'id_to_button_row_buttons');

first i do not see the input when i click the magnifier symbol for wide screens – because you have in your css a rule:

#top  #searchform {
    display: none !important;
}

and that hampers to show the input form !
I know that you want to replace the search there for smaller screens but duplicate ID’s are not good html.

to avoid duplicate IDs add to the code above: $('#menu-menu3').find('form').attr('ID', 'searchform-2');

so that there is then:

function shift_search_icon(){
?>
<script type="text/javascript">
(function($){
	$('#avia-menu').find('#menu-item-search').clone().appendTo('#menu-menu3');
	$('#menu-menu3').find('form').attr('ID', 'searchform-2');
    $('#avia-menu').find('#menu-item-search').remove();
})(jQuery);
</script>
<?php
}
add_action('wp_footer', 'shift_search_icon');

you only had to set the css then for it to:

#top #searchform-2 {
    margin: 0;
    padding: 0;
}

to replace the login logo ( and replace the back link of that logo ) – and to have a background setting on that too:
you can do this on child-theme functions.php:

and before the style is set use ismaels snippet to get the url of the logo:

function my_login_logo(){ 
$logo = avia_get_option('logo'); 
?>
<style type="text/css">
        #login h1 a, .login h1 a {
            background-image: url(<?php echo $logo; ?>);
            height: 100px;
            width: 300px;
            background-size: contain !important;
            background-repeat: no-repeat;
        }
        body.login {
            background-image: url(/wp-content/uploads/LOGIN-BG.jpg) !important;
            background-repeat: repeat;
        }
</style>
<?php 
}
add_action( 'login_enqueue_scripts', 'my_login_logo' );

function custom_loginlogo_url($url) {
  $url = get_site_url();
  return $url;
}
add_filter( 'login_headerurl', 'custom_loginlogo_url' );

you had to find your best dimensions on width and height above

see here: Link

i am always grateful for a link to work on concretely.

By the way dear mods – why does is_home() not working on my test page on that ???
It is a static page – but does not work – only is_front_page() works ?
Does Enfold setting of the front-page not influence the home setting?

i always did it this way:
have a copy for the native language – then translate the layers manually in that copy – and place on the other language that copy. thats all – no plugin needed.

you can style them – but you can use buttons too for that.
To have them beside each other – only a display behavior must set on this
see here an example page for button styling ( even the look is styled there but important for you is that you have button alb and can style each button on it self) put all your buttons ( aligned center ) in a common container and give a custom class to it – rest on that example page:
https://webers-testseite.de/buttons/

the four buttons on that page looks this way in the layout:

no private content for me – because i’m participant as you are.
Please excuse the delayed reaction, sometimes I also have to work and satisfy my own customers.

so again my question : my testpage ( https://webers-testseite.de/cynthia/tuddal/ )
is it the way it should work? Or does your customer have other demands?
See also now the responsive case and behavior of the logo and the other heading links

Later today I will show you how I have implemented the result. Basically it is the integration of the “logo” into the calculation routine of the shrink script.
We will add your Logo not by having a menu list point in the top-menu but only by placing it via child-theme functions.php and absolute positioning.
And this will be the only logo you need for that.
On your page you beginn the logo height at 300px – and it should end at 66px – so shrink-factor is 4.545
you can see here what we need to obtain that in the avia-snippet-sticky-header.js : https://kriesi.at/support/topic/shrinking-of-header-amount-an-info/#post-1044887
With that shrinkfactor we can calculate the two values to influence in the shrink script. The only the thing to do in this script will be the integration of the new “toplogo” to that calculation. No panic i will send you the edited script-file: https://pastebin.com/gi40An1c
Download-link: https://pastebin.com/dl/gi40An1c

But for now enough – detailed info later! IF – you are interested in that solution

do you have a svg on your logo ?
you can see here a playground with your logo – but if we had a svg we could set single parts of the logo to not be seen when the header is scrolled.
https://webers-testseite.de/cynthia/tuddal/

i only have styled it yet for the wider screens – but when you got the svg this comes next.

on the link of the masonry items – you have a class: portfolio_entries-xyz the xyz is the portfolio “category” ( this is actually a taxonomy)

you can place it in a pseudo-container like:
see here: https://webers-testseite.de/pureinstall/portfolio-masonry/
(this was originally a help to place the selection next to the masonry.)

.portfolio_entries-buecher .av-masonry-outerimage-container:before {
  content:"";
  width: 100%;
  height: 100%;
  position: absolute;
  background-image: url(https://webers-testseite.de/pureinstall/wp-content/uploads/Buecher.png);
  background-repeat: no-repeat;
  background-size: 100px;
  background-position: center 30%;
  z-index: 2;
}

and: on posts and categories the class is: category-xyz the category name is the xyz

for background-attachment : fixed
there is a better way to have it – because on IOS Devices – this looks strange – on scrolling it flickers
( google on that background-attachment : fixed and Safari Browsers )

there is a little trick to have that: the background-image that should have background-attachment : fixed goes to the pseudo container :before –
and that container is set to position fixed!
So the code above will look like this ( for my page-id ) :

#top.page-id-38479 {
  background-image: url(https://webers-testseite.de/wp-content/uploads/IMG_bg.jpg);
  background-repeat: repeat;
  background-position: center center;
  background-attachment: scroll;
}

#top:before {
  background-image: url(https://webers-testseite.de/wp-content/uploads/IMG_background_treatments.png);
  background-repeat: repeat-y;
  background-position: left top;
  content: "";
  position: fixed;
  width: 100%;
  height: 100%;
  -webkit-clip-path: inset(0 0 0 0);
          clip-path: inset(0 0 0 0);
}

#top.page-id-38479 #main {
  background-color: rgba(255,255,255,0.2) !important;
}

#top.page-id-38479 .main_color {
  background-color: transparent !important;
}

.html_stretched #top.page-id-38479  #wrap_all {
  background-color: transparent !important;
}

with the fixed image on repeat-y now

First of all – what kind of layout do you have choosen on Enfold: General Layout : a stretched or a boxed or at the end a fixed frame layout?
If you have a boxed layout f.e. – you will have then on General Styling a “Body Background” Option

But this is only one part of your example page.
If you like to have a full transparent content – like on your example page there had to be a lot of css settings to be made.

best would be if you start with that boxed layout – it is possible to have this with a fixed frame.
It is hard to have this with a slideshow in the background..
That was my old attempt to reach this – but the slideshow timing will not be synchronized the more time passes:
https://webers-testseite.de/goldfinger/
( These are two identical slideshows that runs on theory synchronized – the one on top shows only a narrow strip and has a high z-index – the other has a low z-index)
But that is not necessary for your solution with a static background-image.
It will be best to help you if we can see the page it concerns.
it is easy to have a body background-image via quick css f.e. and even to have more than one background-image on the same container:
you see on that page how it is done for a 1/1 container with three background-images and different settings :
https://webers-testseite.de/multiple-background-images/

in other words it is possible to have this http://naturkosmetik-studio.at/Images/IMG_background.png as one background pattern that is set to repeat or not to scroll away – and those leaves too but with no repeat.

maybe you have a /products etc in your bin!
empty that bin and try again