Options Page - Me being bad at WP Settings API

<?php
class vegas{
    public function __construct(){
        if(is_admin()){
        add_action('admin_menu', array($this, 'vegas_add_settings_page'));
        add_action('admin_init', array($this, 'page_init'));
    }
    }

  public function vegas_add_settings_page(){
      add_submenu_page('edit.php?post_type=vegasslider', 'Custom Vegas Settings', 'Settings', 'edit_posts', basename(__FILE__), array($this, 'create_vegas_admin_page'));
        add_action('admin_menu', 'vegas_add_settings_page'); // add the admin options page

   }
 public function create_vegas_admin_page(){
        ?>
    <div class="wrap">
        <?php screen_icon(); ?>
        <h2>Vegas Settings</h2>
        <form method="post" action="options.php">
            <?php
                    // This prints out all hidden setting fields
            settings_fields('vegas_option_group');
            do_settings_sections('vegas-setting-admin');
        ?>
            <?php submit_button(); ?>
        </form>
    </div>
    <?php
    }

    public function page_init(){
    register_setting('vegas_option_group', 'fade_key', array($this, 'check_fade'));
  register_setting('vegas_option_group', 'delay_key', array($this, 'check_delay'));
  register_setting('vegas_option_group', 'overlay_key', array($this, 'check_overlay'));
  register_setting('vegas_option_group', 'title_key', array($this, 'check_title'));
  register_setting('vegas_option_group', 'arrows_key', array($this, 'check_arrows'));
  register_setting('vegas_option_group', 'autoplay_key', array($this, 'check_autoplay'));
  register_setting('vegas_option_group', 'global_key', array($this, 'check_global'));
  register_setting('vegas_option_group', 'id_key', array($this, 'check_id'));

  add_settings_section(
        'setting_section_id',
        'Setting',
        array($this, 'print_section_info'),
        'vegas-setting-admin'
    );

    add_settings_field(
        'Fade',
      'Fade (milliseconds):',
        array($this, 'fade_field'),
        'vegas-setting-admin',
        'setting_section_id'
    );
  add_settings_field(
        'Delay',
      'Delay (milliseconds):',
        array($this, 'delay_field'),
        'vegas-setting-admin',
        'setting_section_id'
    );
  add_settings_field(
        'Overlay',
      'Overlay (Full Image URL):',
        array($this, 'overlay_field'),
        'vegas-setting-admin',
        'setting_section_id'
    );
  add_settings_field(
        'Title',
      'Title:',
        array($this, 'title_field'),
        'vegas-setting-admin',
        'setting_section_id'
    );
  add_settings_field(
        'Arrows',
      'Display Arrows:',
        array($this, 'arrows_field'),
        'vegas-setting-admin',
        'setting_section_id'
    );
  add_settings_field(
        'Autoplay',
      'Autoplay:',
        array($this, 'autoplay_field'),
        'vegas-setting-admin',
        'setting_section_id'
    );
  add_settings_field(
        'Global',
      'Global (Adds the slider to every page/post):',
        array($this, 'global_field'),
        'vegas-setting-admin',
        'setting_section_id'
    );
  add_settings_field(
        'Id',
      'Slider ID (specific to the slider you want to use):',
        array($this, 'id_field'),
        'vegas-setting-admin',
        'setting_section_id'
    );
    }

    public function check_fade($input){

        if( isset($input['Fade'])){$Fade = $input['Fade'];}

        if( !isset($Fade['Fade']) && isset($input['Fade']) && is_numeric($input['Fade'])){
        if(get_option('fade') === FALSE){
        add_option('fade', $Fade);
        }else{
        update_option('fade', $Fade);
        }
    }else{
        $Fade = '';
    }
    return $Fade;
    }

  public function check_delay($input){

    if( isset($input['Delay'])){$Delay = $input['Delay'];}

            if( !isset($Delay['Delay']) && isset($input['Delay']) && is_numeric($input['Delay'])){
                if(get_option('delay') === FALSE){
        add_option('delay', $Delay);
        }else{
        update_option('delay', $Delay);
        }
    }else{
        $Delay = '';
    }
    return $Delay;
    }

public function check_overlay($input){

  if( isset($input['Overlay'])){$Overlay = $input['Overlay'];   }

          if(!isset($Overlay['Overlay']) && isset($input['Overlay']) &&!is_numeric ($input['Overlay'])){
        if(get_option('overlay') === FALSE){
        add_option('overlay', $Overlay);
        }else{
        update_option('overlay', $Overlay);
        }
    }else{
        $Overlay = '';
    }
    return $Overlay;
      }

  public function check_title($input){

    if( isset($input['Title'])){$Title = $input['Title'];   }

          if(!isset($Title['Title']) && isset($input['Title']) && !is_numeric ($input['Title'])){
        if(get_option('title') === FALSE){
        add_option('title', $Title);
        }else{
        update_option('title', $Title);
        }
    }else{
        $Title = '';
    }
    return $Title;
      }

   public function check_arrows($input){

   if( isset($input['Arrows'])){$Arrows = $input['Arrows'];     }


   if ( !isset( $Arrows['arrows'] ) ) {
     $Arrows = 0;
     add_option('arrows', $Arrows);
   }

    if ( $input['Arrows'] == 1 ) {
        $Arrows = 1;
      update_option('arrows', $Arrows);
    } else {
        $Arrows = 0;
      update_option('arrows', $Arrows);
    }
   return $Arrows;
}

   public function check_autoplay($input){

    if( isset($input['Autoplay'])){$Autoplay = $input['Autoplay'];  }

    if ( $input['Autoplay'] == 1 ) {
        $Autoplay = 1;
      update_option('autoplay', $Autoplay);
    } else {
        $Autoplay = 0;
      update_option('autoplay', $Autoplay);
    }
   return $Autoplay;
}

   public function check_global($input){

    if( isset($input['Global'])){$Global = $input['Global'];    }

    if ( $input['Global'] == 1 ) {
        $Global = 1;
      update_option('global', $Global);
    } else {
        $Global = 0;
      update_option('global', $Global);
    }
   return $Global;
}

    public function check_id($input){

      if( isset($input['Id'])){$ID = $input['Id'];  }

        if(!isset($ID['Id']) && isset($input['Id']) && is_numeric($input['Id'])){
        if(get_option('id') === FALSE){
        add_option('id', $ID);
        }else{
        update_option('id', $ID);
        }
    }else{
        $ID = '';
    }
    return $ID;
    }

    public function print_section_info(){
    print 'These settings help define the shortcodes that are generated for you when you create a slide and are used exclusively if you use the global option. Enter your settings below:';
    }

    public function fade_field(){
        ?><input type="text" id="fade" name="fade_key[Fade]" value="<?php echo get_option('fade'); ?>" /><?php
    }
    public function delay_field(){
        ?><input type="text" id="delay" name="delay_key[Delay]" value="<?php echo get_option('delay'); ?>" /><?php
    }
    public function overlay_field(){
        ?><input type="text" id="overlay" name="overlay_key[Overlay]" value="<?php echo get_option('overlay'); ?>" /><?php
    }
    public function title_field(){
        ?><input type="text" id="title" name="title_key[Title]" value="<?php echo get_option('title'); ?>" /><?php
    }
    public function arrows_field(){
      $Arrows = get_option('arrows');
      if($Arrows == 1) { $checked = ' checked="checked" '; }
      else{ $checked = '';}
                       echo '<input type="checkbox" id="arrows" name="arrows_key[Arrows]" value="1" '.$checked.' />'; //<333333
    }
    public function autoplay_field(){
      $Autoplay = get_option('autoplay');
      if($Autoplay == 1) { $checked = ' checked="checked" '; }
      else{ $checked = '';}
                       echo '<input type="checkbox" id="autoplay" name="autoplay_key[Autoplay]" value="1" '.$checked.' />';
    }
    public function global_field(){
      $Global = get_option('global');
      if($Global == 1) { $checked = ' checked="checked" '; }
      else{ $checked = '';}
                       echo '<input type="checkbox" id="global" name="global_key[Global]" value="1" '.$checked.' />';
    }
    public function id_field(){
      $Global = get_option('global');
        ?><input type="text" id="id" name="id_key[Id]" value="<?php echo get_option('id');?>" <?php if($Global != 1){echo 'disabled="disabled"';} ?> /><br/>
<p>Note: You have to set the global option and save before you can add the id.  Also the id is neccessary if you're going to use the global option.<br/>  You can find the id on the slide page (where you added the photos)</p>
<?php
    }
}

$vs_enet = new vegas(); ?>