While this is not possible in Animator, you could draw an element styled as a half-circle and then scale it vertically to achieve the same effect as in your video. I've created a little project demonstrating it - you can get it on github here: https://github.com/mbojic/example_mouth
If you don't use github, you can click 'Download ZIP'
Animator is based on CSS3 animations, and giving that bezier curves cannot be created as HTML elements currently, this is not a feature that will be added any time soon. Bezier, and other curves can be drawn inside a SVG element, however CSS3 would apply only to the container SVG element, and not to the inner elements.
As for butterfly - absolutely! You can create exact same animation with Animator, following basically the same steps. I created a quick project with a butterfly fluttering around - you can find it here: https://github.com/mbojic/example_buttefly