What is the best way to create an animation path around a central object like a mountain in Google Earth? At the end I think the animation path should be a "tour" to create video file from it.
One option (not elegant but quick) is to view the locale in GE, then press SHIFT + LEFT/RIGHT ARROW KEY. Try this and you'll get a feel for best view angle, etc. Once you get good at that, use the Record-a-Tour button on the toolbar to record your motion. Save the tour and you'll see it appear in your My Places. Then if you want to view the code you've just created, save the tour from your My Places to a KML file that you can view in a text editor.
What you'll see in the KML file is a gx:Tour and gx:Playlist and a series of gx:FlyTo's. Either learn from that code, or perhaps even just keep the code as is.
I've learned a lot from Google's KML documentation at https://developers.google.com/kml/documentation/kmlreference
If you want, Google Earth Pro -- recently made freely available -- will export your tour to video.