Why can I create more than one Acquia Cohesion template for the full view mode?
You can create more than one template to provide layout and style alternatives with the use of the template selector.
Acquia Cohesion renames to Site Studio from version 6.2. Tell me more.
The Youtube video embed is responsive so it should expand to the width of its parent. If you do need to set a width you can apply the Width CSS property through the Style Builder.