Are there programs to create and edit SVG animations?
Looks like there is a standard open format for vector animation: SVG.
How to create and edit such files?
I expect something like Blender with keyframes and curve editor. Inkscape does not seem to have animation abilities at the first glance.
FOSS is strongly preferred (so Flash-related things are discouraged, but if there is a Flash to animated SVG converter it should be mentioned).
Here there is a list of already existing animation programs (including SVG animation) http://wiki.inkscape.org/wiki/index.php/Animation-%28Timeline%29
There are both FOSS and proprietary ones.