Yes and no.
You can create custom audio controls for you video. You will need to create an Action Sequence that sets the volume property. But you might encounter issues of you are looking to recreate a volume slider. This would where a little code via Flash Builder would save the day.
The Full Screen functionality is not accessible to my knowledge with Flash Catalyst. This would have to dealt with entirely within Flash Builder.
Hope this helps,
In the new Panini preview version, it's possible to write a custom skinnable component in Flash Builder that handles all the behavior, and then visually skin it in Catalyst.
For example, here are two custom skinnable components over on FlashCats
A simple skinnable video player
A button to make your application fullscreen
You would probably want to customize these in Builder for your specific scenario, but they're a start.