It is certainly intended that your windows should remember their positions when you reopen a project, but things can get confused if you switch between single and multi-display setups.
Fingering is definitely a high priority and I hope we’ll be able to do some work on this in the same update that we are targeting for percussion and cues, but I can’t guarantee it at this stage, I’m afraid.
I too would love to see this feature. My temporary workaround has been to create a dedicated paragraph style for my fingering numbers and shift-X it wherever they are necessary. At least if you apply a paragraph style you know you have consistency.