what do you think about this Zbox fanless?
Are AMD Kabini A4-5000 or Intel Baytrail capable to running home/office apps, Google Earth, full HD video and similar things?

Yes but...
Drivers may or may not be a problem. Make sure there are good drivers for your OS. Intel in particular has released some poor graphics drivers for its low-power chips of late. It shouldn't be a problem in the long run with Bay Trail but better make sure!
Google Earth is supposed to run on crappy hardware... but how well does it run on that? I don't use it but in general the chips you mention are pretty good, better than many people assume and about as good as the most powerful hardware I normally use. But they do have limitations. I don't do 3D stuff like Google Earth for instance.

Typical use of home/office apps and reasonably encoded "full HD" videos don't require much power. Older stuff would be fine. There'd be no point in paying for new stuff if that was the only thing you were planning to do

i think Atom D510 it's enough for apps above listed, and BayTrail and Kabini should be even better, right?

Google earth will run just fine on Baytrail or Kabini, it really isn't that demanding.

I've personally run it in the past on systems with Intel "Extreme Graphics", 810 to 865 chips. It wasn't too bad if you didn't turn on too many options or 3D buildings. To be fair that was older versions, the current release may not run on such ancient hardware.

I have run the current release on systems with the GMA950 and single core Atoms (N270) and it runs acceptably. Baytrail or Kabini should have no problems.

here they go: http://www.zotac.com/en/products/mini-pcs/c-series/product/c-series/category/mini-pcs/main-category/mini-pcs.html

Yeah - just saw a couple of the Computex press releases for this. Hopefully, Zotac will seed review sites with samples so we can find out the thermal performance.

Are all of the C-Series models fanless? Even the Core i5 model?

http://liliputing.com/2014/06/zotac-zbo ... i-pcs.html

the only question is the graphics card HD4200: for you is valid to play fullhd video, Google Earth, video offline, multimedia light?