The polygon and 3d model demos should answer both of your questions:
http://cesiumjs.org/Cesium/Apps/Sandcastle/index.html?src=Polygon.html&label=Geometries
http://cesiumjs.org/Cesium/Apps/Sandcastle/index.html?src=3D%20Models.html&label=Showcases
I would also recommend taking a look at the Visualizing Spatial Data tutorial: http://cesiumjs.org/2015/02/02/Visualizing-Spatial-Data/
If you are still having problems, let us know.