The examples on the GitHub repo (like this basic one: http://vizicities.com/demos/basic/) use an OpenStreetMap tile endpoint provided by Mapzen and so will work anywhere in the world. The caveat being that the OpenStreetMap data varies in quality around the world. However, in that case you could use a better quality GeoJSON-based dataset for the area you're interested in if it exists.
Countryside rendering depends on what you want to see. You may not see many buildings but you'll see the underlying map on the 2D basemap and you can always decide to output (or ignore) specific things like roads or fields or trees. This obviously depends on whether that data exists and exactly how you want to output it.
By default ViziCities can't do anything with LIDAR data yet but it's on the list of things to add in the future.
There will be soon, yes. Right now the ground is flat in ViziCities but there are plans to add 3D terrain, though it's not a simple feat. It's possible to extend ViziCities to do this yourself.
