How do I make a integrated search service site?

Question

I want make a integrated search service site. I referenced this and this. There are a few problems.

HTML :

<div id="integrated_search_form">
      <form>
          <input type="search" name="" id="integrated_search_word">
          <input type="submit" value="search" id="integrated_search_button">
      </form>
  </div>
<div id="search_result_website_div01">
    <form>
        <input type="text" name="" id="website_url_01">
        <input type="submit" value="submit">
    </form>
    <object id="myobj" data="" type="text/html">Not loading</object>
</div>

JS :

<script src="https://code.jquery.com/jquery-3.4.1.js"></script>
<script>
    //
    $(document).ready(function(){
        //
        var $dynamic_integrated_search_word = $('#integrated_search_word');
        var $dynamic_url_01 = $('#website_url_01');  // https://en.wikipedia.org/wiki/

        $('#myobj').attr('data', $dynamic_url_01)    // Problem 1
        .css({
            width: 400,
            height: 300,
            background: 'gray',
            overflow: scroll
        });


        // Problem 2
        /*
         $('body').find('input[type = search]').val('wiki');
         $('body').find('input[type = search]').parents('form').submit();
        */

        // Problem 3 - under 3 things not working all.
        /*    
        .console.log($('body').find('input[type = search]').val('wiki'))
        .contents().find('input[type = search]').val('wiki')
        .load(function(){
           $(this).contents().find('input[type = search]').val('wiki')
       });
        */
    });

Problem 1: object 'data' attr insert static value(?) like 'https://en.wikipedia.org/wiki/' is working well. But when I insert dynamic variable is not working.

Problem 2: Entered the following sentence in the developer tool's console.

// $('body').find('input[type = search]').val('wiki');
// $('body').find('input[type = search]').parents('form').submit();

this works well on wikipedia, but it doesn't work on Google or any other wiki sites.

Problem 3: I want to produce the same result by JQuery as I entered the following sentence in the developer tool's console at each site.