1. The StaticBatcher -> Empty GameObject -> Sprites scenario is a bug. This has been fixed in the next release, but for now:
You can fix it in tk2dStaticSpriteBatcherEditor.cs, right at the end of the function,
if (baseSprite != null) {
baseSprite.scale = bs.baseScale;
baseSprite.color = bs.color;
}
2. Nested static batchers aren't supported, and intentionally so. Its far to hard to handle every possible permutation here correctly, and still get the gains of the batcher.
3. This looks like a fairly recent bug - it actually does transfer the data to the children, but doesn't update the meshes. I'll fix it for the next release, but for now, if you press play, reload the scene, etc. it should update.