Can I add widget in pages and posts without any plugin or additional codes

Hi,
yes, you can.
For the search widget,

function post_searchform( $form ) {
    $form = '<form role="search" method="get" id="searchform" action="' . home_url( '/' ) . '" >
    <div><label class="screen-reader-text" for="s">' . __('Search for:') . '</label>
    <input type="text" value="' . get_search_query() . '" name="s" id="s" />
    <input type="submit" id="searchsubmit" value="'. esc_attr__('Search') .'" />
    </div>
    </form>';

    return $form;
}

add_shortcode('mysearch', 'post_searchform');

For the text widget, add your text widget content inside the shortcode function.

I placed the code in functions.php of child theme, then I add a text widget in footer widget area and put [mysearch]. But didnt work for me. But it is working in pages when I adding this short code.

https://ordinary1.esy.es/wordpress1/