Sticky Mobile Menu

Hi Roman.

I don’t think that it will cover most of the whole screen. It will keep just a menu bar with mobile menu icon on top of the screen.
Very similar to the code provided by your colleague for Sydney theme:

jQuery(function($) {

  if ( matchMedia( 'only screen and (max-width: 1024px)' ).matches ) {

    var headerFix = $('.site-header').offset().top;
    var vDistance = headerFix+280;

    var inserated = false
    $(window).on('load scroll', function() {
      var y = $(this).scrollTop();
      if ( y >= vDistance) {

        if(inserated == false){
          var newHead = $('#masthead').clone();
          
          (newHead).prependTo('body').addClass('masthead-clone').animate({
            top: 0
          }).resize();

          $('.masthead-clone .btn-menu').on('click', function() {
              $('.masthead-clone #mainnav-mobi').slideToggle(300);
              $(this).toggleClass('active');
          });

          $(document).on('click', '.masthead-clone #mainnav-mobi li .btn-submenu', function(e) {
              $(this).toggleClass('active').next('ul').slideToggle(300);
              e.stopImmediatePropagation()
          });          
          
          inserated = true;
          
        }    
        
      } else {
      
        $('.masthead-clone').animate({
          top: -200
        }).remove();
        inserated = false;
        
      }

    });
  
  }

});

Ok Roman.

I will do it by myself.
But please, could you look into issue with jumping banner part when you first start scrolling the page on mobile screen.
It will be easier for me to do the rest, If you will fix the bug first.

Thanks