Video Production: How can I add smart graphics/animation to live-action footage?

This is just simple compositing, as far as I can see.  The answer is that you create the graphics as a separate movie (what we call a http://en.wikipedia.org/wiki/B-roll in  film.) You make this  in any animation software you wish, though some software is made for titling and will thus be easier to use. Then you take both movies into a digital editing package that has http://en.wikipedia.org/wiki/Digital_compositing features and assemble the two movies into a single output.

I do not know about FCP but on Premiere, I can use Photoshop to create those overlays with black blackground (black blends in easily compared to other colors). Then superimpose the created JPG/GIFs where I want them to appear (on a separate track). Then use "keying" to remove the black background so that main video is visible without cutting off the superimposed images. I hope there are similar options available in FCP. I haven't seens its interface but since it is said to be much better than Premiere, there should be similar or better options.