How to customize video player (autoplay and such) ?

The oEmbed protocol itself only defines the maxwidth, maxheight and format parameters but each provider may support additional custom parameters. So you may be able to do some customization, depending on whether a provider accepts a parameter for autoplay, play chrome colour, etc. Otherwise you can try to parse the response and alter the HTML or you may be better off with a single provider module such as Media: YouTube, Media: Vimeo, etc which will generally provide more customization as they work with provider-specific APIs.

You can implement hook_media_oembed_request_alter() to alter the request to the oEmbed endpoint and hook_media_oembed_response_alter() to alter the response.

Here's an example with youtube...

/**
 * Implements hook_media_oembed_response_alter().
 */
function custom_media_oembed_response_alter(&$response) {
  if ($response['provider_name'] == 'YouTube') {
    // Use the highest resolution youtube thumbnail when generating images.
    $response['thumbnail_url'] = str_replace('hqdefault', 'maxresdefault', $response['thumbnail_url']);

    // Use 720p default quality with autoplay in lightboxes.
   $response['html'] = str_replace('?feature=oembed', '?autoplay=1&vq=hd720', $response['html']);
  }
}

It's terrible but a limitation of how oembed works.

codesidekick++ Thanks, that is great.