custom comment fields inside custom post type

I have a custom post type and I want to create 2 new fields and remove the default ones (author,url,email) without affecting the default comment fields inside the blog posts.

Also I want to make it visible just for logged in users, with a message like this for non-logged in users:

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I’ve noticed that I can do this from the dashboard setting but the problem is that this will be applied to all the comments and I want to apply this just on a specific CPT.

So, here is my approach:

function debate_comment_fields( $fields ) {

 if( is_singular( 'debate' ) ) {

     $fields['url'] = '';
    $fields['author'] = '';
    $fields['email'] = '';

    $fields['first'] = '<p class="comment-form-first"><label for="first">' .
                     __( 'HTML5' ) .
                     '</label>' .
                     '<input id="first" name="category" type="radio" value="'.get_post_meta($post->ID, 'agree', true).'" /></p>';

    $fields['second'] = '<p class="comment-form-second"><label for="second">' .
                       __( 'FLASH' ) .
                       '</label>' .
                      '<input id="second" name="category" type="radio" value="'.get_post_meta($post->ID, 'disagree', true).'" /></p>';

    return $fields;

}
}
add_filter('comment_form_default_fields','debate_comment_fields');

This code is removing the default fields also on the blog posts and I don’t want this.
After I submit a comment inside my CPT I get this:
ERROR: please fill the required fields (name, email).

And also how can I add a message if the user is not logged in like this:

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just on my CPT.