Add Additional File Info (jpeg compression & file size) settings to Edit Images Screen

You can try to use the attachment_submitbox_misc_actions filter to add more info to the box. Here is an example for the filesize part:

add_action( 'attachment_submitbox_misc_actions', 'custom_fileinfo_wpse_98608' );
function custom_fileinfo_wpse_98608(){
    global $post;
    $meta = wp_get_attachment_metadata( $post->ID );
    $upload_dir = wp_upload_dir();
    $filepath = $upload_dir['basedir']."https://wordpress.stackexchange.com/".$meta['file'];
    $filesize = filesize($filepath);
    ?>
    <div class="misc-pub-section">
        <?php _e( 'File Size:' ); ?> <strong><?php echo $filesize; ?> </strong> <?php _e( 'bytes' ); ?>             
    </div>
<?php
}

The default file info is displayed with the attachment_submitbox_metadata() function through this action:

add_action( 'attachment_submitbox_misc_actions', 'attachment_submitbox_metadata' );

in the file /wp-admin/includes/media.php