[TimeZone]

Anyone knoe where can I download the default animated background? Is it possible to use it with other skins skin?

You can find the image here from the official github repo for the skin.

Unfortunately for you, the image is not animated and this answers your second question if you can use it in another skin. The skinner is using some really nice trick to change the colours creating an illusion that the image is animated. I can't go into details because I don't know how he achieves this. All I can say is Bravo Manfeed, I also thought it was an animation all along! WOW!

I said this answers your 2nd question because unless you know how he is doing it, you can't add the image to another skin and expect it to work, all you will get is a still image. Me answering your question does not mean am an expert, I am just trying to help in the spirit of KODI community, my answers can be completely wrong.