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Several of those questions are rather difficult to answer immediately, without further information. But this much can be said at once:
1. scripting for more or less what you describe can be included.
2. I don't know what you mean by a 'delayed' button.
3. autoplay for video included is routine.
4. I'm not sure which overlay items you mean, but there may be a video file playing plugin that does that.
5. fastest playback is helped by lowering the density of the video. The grainier the video, the faster it will play.
There is this, the basic answer to your question:
And then there are all these to choose among:
If this answers your question, please rate my answer. Thanks.
I admit I don't have the information you need, so I have Opted Out of this case, opening your request in your last posting to other Experts.
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First of all the functions you want to implement are possible with Wordpress. I am not clear about point 2 "Delayed button" do you mean a Preview button to preview video ? If you have any sample link please provide.
With the help of WP Exit Page Redirect you can show a notification and redirect to a default page when users leaving a page on your site. Download that plugin from https://wordpress.org/plugins/wp-exit-page-redirect/
Use the plugin You List to embed Youtube Videos. That plugin have options to hide Youtube controls and branding.