Somehow my code based on Settings API doesnt work OK, can't figure out why

It think I do everything as it is said in descriptions and tutorials, but still I don’t have any options displayed on my options page and I don’t understand why.

Well, at first at the beginning of functions.php I include the file with Settings-API-based code:

require_once 'aboutsite.php';

Then I add those 3:

add_action('admin_menu', 'aboutus_menuitem');
add_action('admin_menu','myoptions_save_settings');
add_action('admin_init','prepare_settings');

The I registration of settings, sections and fields:

function prepare_settings(){
    register_setting('myoptions','myoptions');

    add_settings_field('aboutsite', 'Aboutsite', 'myoptions_settings_aboutsite_content', 'sinkevich','aboutsite');
}

Then the “main” page function:

function aboutus_menuitem(){
    add_menu_page('About the site', 'About the site', 'read', 'aboutsite','aboutsite_page',NULL,11);
}

function aboutsite_page(){
    ?><div id="wrap">

    <?php if ( isset( $_GET['setting-updated'] ) ) echo '<div class="updated"><p>Options saved</p></div>';?>    

        <form action="admin.php?page=aboutsite" method="post">
            <?php
                settings_fields('myoptions');
                do_sections('myoptions');
            ?>
            <input name="myoptions_aboutsite[submit]" type="submit" class="button-primary" value="Сохранить" />
        </form>

    </div><?php

}

And the last, functions that do the code of the input fields, textareas, etc:

function sinkevich_settings_aboutsite_section() {

}

function sinkevich_settings_aboutsite_content(){
    $options = get_option('sinkevich');
    ?>
    <textarea name="aboutsite"><?php echo $options['aboutsite']; ?></textarea>
    <?php
}

Then, I run the site and see a new menu page, click it and theres is no fields there. There is a form in the code generated, but there’s only:

<form action="admin.php?page=aboutsite" method="post">
            <input type="hidden" name="option_page" value="myoptions"><input type="hidden" name="action" value="update"><input type="hidden" id="_wpnonce" name="_wpnonce" value="abbb1ca570"><input type="hidden" name="_wp_http_referer" value="/wp-admin/admin.php?page=aboutsite"></form>