(1)

var store = App.TreePanel1.getStore(),
node = store.getNodeById("Node1");
 
node.appendChild({
text : "The New Node",
leaf : true
})
 
(2)
 
var sm = App.TreePanel1.getSelectionModel();
selectedNode,
parentNode;
 
if (sm.hasSelection()) {
selectedNode = sm.getSelection()[0],
parentNode = selectedNode.parentNode;
}