We cannot edit templates and themes on free hosted WordPress.com blogs. It’s not possible to move elements like where the menu dispalys without purchasing an annually renewable custom design upgrade and doing the required CSS editing.
Maybe try switching over to the text editor instead of the visual editor when editing the post. If you paste the YouTube link there, you’re sure to not have it automatically linked and break the oEmbed. There’s some good instructions at http://en.support.wordpress.com/editors/ but keep in mind this article calls it the HTML editor, and the name recently changed to text editor.