How can I delete empty load cases and rearrange the remaining ones?
If you use the navigator, go to "Load Cases and Combinations" -> "Load Cases" and right-click the load case that you want to delete. Then, select "Delete" in the context menu.
Moving up the next load case automatically as a substitute for the deleted one is not possible. For this you must rename the successive load case. Do this by using the right mouse button and select "Edit" in the context menu.
Deleting load cases is easier with the above mentioned "Model Data". In the "Model Data" dialog box, you can delete individual load cases in the "Load Cases" tab. With the button "Edit Load Case" you can rename the other cases.