As a participant i could not see private content.

why do you think that there is something wrong?
is on your dropdown list no custom svg ?

you know how to have a child-theme replacement script?

you have found the solution on the element itself? – because i see images on your tabs.

is this a transparent header on desktop view?
then you had to adjust on fixed non-transparent header the padding-top of #main

but for your trials to have sticky header on mobile – my advice is to erases the code and replace it with ( It is difficult to identify the issue with the existing code. Therefore, I would prefer to start over.) :

@media only screen and (max-width: 1023px) {
    #header {
        position: fixed !important;
        height: 120px !important;
        max-height: 120px !important;
    }

    #top #header.av_header_transparency #header_meta {
        background-color: transparent;
    }

    #header_main {
        border-bottom: none;
    }

    #header:not(.av_header_transparency) #header_main {
        box-shadow: 0 5px 5px rgba(182,182,182,0.75);
    }

    .responsive #top .av-logo-container ,
    .responsive #top .logo a,
    .responsive #top .logo img,
    .responsive #top .logo svg {
        height: 120px !important;
        max-height: 120px !important;
        line-height: 120px !important;
    }

    .responsive #top .av-main-nav .menu-item-avia-special a {
        height: 120px !important;
        line-height: 120px !important;
    }  

    .responsive.html_mobile_menu_tablet #top #wrap_all .av_header_transparency {
        background-color: transparent !important;
    }

    #top .header_bg {
        background-color: transparent !important;
    }

    #top #header:not(.av_header_transparency) .header_bg {
        background-color: #FFF !important;
    }

    .responsive.html_mobile_menu_tablet #top .av_header_transparency .logo img.alternate, 
    .responsive.html_mobile_menu_tablet #top .av_header_transparency .logo .subtext.avia-svg-logo-sub {
    display: block !important;
    }

    .responsive.html_mobile_menu_tablet #top .av_header_transparency.av_alternate_logo_active .logo a > img, 
    .responsive.html_mobile_menu_tablet #top .av_header_transparency.av_alternate_logo_active .logo a > svg {
    opacity: 0;
    }

    /*** das hier individuell anpassen je nach dem  ***/
    #top #header.av_header_transparency #header_meta .phone-info * {
        color: #FFF !important;
    }

    .html_mobile_menu_tablet .header_color  #header.av_header_transparency div .av-hamburger-inner, 
    .html_mobile_menu_tablet .header_color  #header.av_header_transparency div .av-hamburger-inner::before, 
    .html_mobile_menu_tablet .header_color  #header.av_header_transparency div .av-hamburger-inner::after {
        background-color: #FFF;
    }
    .html_mobile_menu_tablet .header_color  #header.av_header_transparency .menu-item-search a:before {
        color: #FFF;
    }
    .responsive.html_header_top.html_mobile_menu_tablet  #top #main {
        padding-top: 120px !important;
    }
    .responsive.html_header_top.html_header_transparency.html_mobile_menu_tablet  #top #main {
        padding-top: 0 !important;
    }
}

and next: synchronise the switch point of your burger menu with those settings for your header.
means

@media only screen and (max-width:1023px) {
  #avia-menu .menu-item {
    display:none
  }
  .av-burger-menu-main.menu-item-avia-special {
    display:block
  }
}

for your content inside the first section there should be more distance to header on smaller screens! …
in addition :

@media only screen and (max-width:767px) {
  .responsive.html_header_top.html_header_transparency.html_mobile_menu_tablet  #top #main #av_section_1 .content {
    padding-top: 150px
  }
}

and what if you switch temporarly to a standard theme. Do the wp-admin buttons show the same problem?

do you have only standard entries in your htaccess file – or are there additional custom rules inside?

yes – and it is under Tools->Site Health->Info->Database

And you have choosen that setting on : General Layout – Content Alignment : “Center Content”

it is just below that option where you have choosen the left sidebar header

can you mail me the link too – if you do not like to make it public

do you use WPML on that page?

see for example: https://kriesi.at/support/topic/header-structure/
and there is a link to e.g. synchronise the languages https://kriesi.at/support/topic/implementing-the-same-theme-setting-to-all-languages-using-enfoldwpml/

I think this symbol appears when an image or file cannot be found.

Edit : now i have inspected your page with dev tools – my pages with full-width easyslider and video inside as list item – looks totaly different to your DOM.

I got this <div id="mep_0" … container inside <div data-rel="slideshow-1" class="avia-slide-wrap " ….with all the video instructions inside

Ah ok : this seems to be a matter if the inserted url is a relative url and not an absolute url.
by the way it seem to be the only way to show the video on iPhones by relative urls – but than a message is shown : av-fallback-message if there is no fallback image.

so try: let there be the relative url to your video – do not enter a fallback image and:

#top .av-fallback-message,
#top .av-fallback-message + img {
  display: none !important;
}

or if you do not like to use the Sibling Combinator :

#top .av-fallback-message {
  display: none !important;
}
.avia-slideshow li img[src*="undefined"] {
  display: none !important;
}

Check what page-id is it where you do not like to show it – and then :

#top.page-id-12345 .my_title_container {
  display: none;
}

However, if you only want this feature on all pages but not on archive or post pages, for example, you can modify the snippet accordingly.

have a look if this is the default border-top of container_wrap – try:

#top .container_wrap {
  border: none !important;
}

One problem that could arise is if you have different logotypes. For example, the standard logo and alternative logo are SVG files, but the one on this page should be a PNG instead. As long as you stick to one type, there shouldn’t be a problem.

the color of the menu you can redeclared like this :
( because i do not see private content area – here with example page-id’s)

#top.page-id-44112 #header.header_color.av_header_transparency .av-main-nav > li > a .avia-menu-text {
  color: red;
}
#top.page-id-44112 #header.header_color.av_header_transparency .av-main-nav > li > a:hover .avia-menu-text {
  color: yellow;
}

you can replace the alternate logo (that for transparency) : you need to know the ID – if you replace a svg with a png file you had to know the url too of that replacement logo.
put this to your child-theme functions.php (replace the page-id and the other parameters)

function av_change_transparency_settings($header){
  if( is_page('44112') ){
	// add class to the #header for using alternate logo (It's important to leave a space at the beginning within the quotation marks.)
    $header['header_class'] .= ' av_alternate_logo_active';  
	// url of the replacement logo
    $header['header_replacement_logo'] = "/wp-content/uploads/globe-color.png";
	// the id of the replacement logo - check on media library list view
    $header['header_replacement_logo_id'] = 49022; 
  }
  return $header; 
}
add_filter('avf_header_setting_filter','av_change_transparency_settings');

setting that extra class av_alternate_logo_active is not needed if you have a standard transparency logo set on enfold options.
maybe: you had to set some extra css for png logo on width and height on responsive case

see example page here: https://webers-testseite.de/bg-video/

PS: you see on my other pages (f.e. the landing page/home) of that example installation – that i do not use the transparent logo. Because i use svg files – i can fill the letters differently for transparent header. That is the reason why i had to add that extra class on that example page.