Do I have to use IMCE?
No. Acquia Cohesion allows the site builder to select, either use of IMCE or Entity browser for browsing and selecting images.
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.