Sometimes, while shooting a political video, certain persons identity need to be protected. Thus, I would need to bur a face in some way. But how?

cut it out

It's quite a bit of work when the persons are moving. Check out these Youtube-videos for advice:

Face Blur Effect

How to blur out faces and logos in final cut

I do not know if iMovie has anything equivalent, I do not think so.

With FCE you can blur/distort areas, it just does not offer any motion tracking capabilities, so you might end up adding hundreds of keyframes manually. If you need that often, have a look at this FCE plug-in , it works quite well. Of course, Motion 3 in the Final Cut Studio box can do that "out-of-the-box", but using FCE and this plug-in is a decent alternative.