I've drawn a workflow/process diagram in draw.io, but each time I make small changes I have to move everything else around. Is there anything that automatically re-positions the diagram when I make such changes?
Look in the menu under Arrange → Layout. For a process you probably want one of the flow layouts. You can select the swimlanes or members of the swimlanes and apply the flow layout in the direction you want in each case.
When adding an element you can just pull the mouse over and you can see some points appears on the edges, and a big arrow in the middle of the shape. drag any point of them or the arrow and see what happen. in this case when adding elements they will be associated together.