2.) How should I divide my controls into what sort of views?
Create a view with #MainDiv, #TreeDiv and #DatagridDiv. Let #TreeDiv host your tree control (You already know this). Create a partial view to display the datagrid with employee objects. Let #DatagridDiv host this partial view.
Now when a department is selected in tree control, you can make an ajax call to a controller method which accepts the department and returns the partial view containing the employee data. Update the #DatagridDiv with returned data.
Alternatively if you are comfortable with Json, your controller method could return the employee data in Json format (instead of partial view) and You can populate this into an html table inside #datagridDiv using javascript/jquery.
1.) What kind of object should my Index method return to display this aggregated data in the view?
In the Index method you can return your view which contains all 3 Divs and #TreeDiv populated with tree control. On the client side when page loads you can identify the selected department to make an ajax call and update #datagridDiv. This approach will have a it lag on the clientside, however you can use that to display some animation indicating the page is loading/div is updating.
If you dont want to add this lag period, identify the department that will be selected when tree view is loaded and populate the partial view for that department, add this to your #datagridDiv on the server side and deliver.