Items are expanded when they match the filtering criteria.

Once I added the filterdescriptor, the tree started to expand itself
and when I put a break point in RowIsExpandedChanged event handler
the treelistviewrow's IsExpanded property is already true

Can you have a look at the attached sample application
and try to achieve the following:
1. keep the on demand load (so only loadchildren when user clicked on the arrow to expand)
2. apply filter only on the expanded nodes

Currently, the RadTreeListView control does not fully support the merged cells functionality due to the different levels of the hierarchy of the items displayed by the control. 

Currently, setting HierarchyIndent property does not work as expected for nested rows.

Reproducible on http://demos.telerik.com/silverlight/#TreeListView/TreeListViewDragAndDrop

As a workaround you can try executing the selection in a Dispatcher with DispatcherPriority.Render.
This may not apply in the case when there are many nodes outside the View area. 

The goal is to expand a second node each time you expand a particular node from the RadTreeListView. The data of the second node is loaded on demand, but it is not shown when the node itself is expanded.

Keyboard navigation stops working when setting SelectionMode to "Extended", SelectionUnit to "Cell"  and pressing twice the down keyboard key . 

The problem should be resolved with version Q1 2016. 

TreeListView is trying to expand its item which is empty.

There are large number of items for the TreeList (for example 3000) and you have all them initially collapsed.
For example you could modify the IsExpandedBinding demo to have 3000 items.
Then scroll down so the row with Drinks and Count = 2194 is at the top of the control and expand it.
The result is that both that row and the row with Drinks and Count = 2199 expand.