I got them both figured out eventually (including the bonus question...)
First add this to your head section of the page:
<meta name="viewport" content="width=device-width, user-scalable=no">
Then use the following iFrame include from YouTube to insert the video:
<iframe width="100%" height="215" src="http://www.youtube.com/embed/**********?rel=0&controls=0&showinfo=0" frameborder="0" allowfullscreen></iframe>
Replace the asterisk(*) with your video code.
It's very important that you set the iFrame width to 100% or it will mess up your entire page.
That works perfectly.
The only problem is setting the iFrame height, but that will have to be figured out next time.