Is it possible within JME to move the vertices of a 3d model? An example would be this movie: http://www.youtube.com/watch?v=5UtRNF71F0o
yes, you can get the Vertexbuffer from a Geometry and then (as an example) you can iterate over all vertices and pick some out where, say, the Y value is higher than that of marios nose. those vertices can then be moved by, say, the movement of the mouse. 
This is great news… but does jME also expose methods to create new geometries in code at runtime?
you can create geometries at runtime … take a look at Ribbon or TrailMesh.
Excellent – thanks!