Enhance Properties panel: auto hide/reveal panel at appropriate times

[zalexzperez]

Viewing area is greatly reduced when the Properties panel is visible with a standard size. Many times, it's just showing "Nothing selected". So first impulse is to make it smaller so it's not in the way.
But then a widget needs to be edited and... the Properties panel is too small and needs to be resized again.
This creates an annoying workflow.

What if when nothing is selected (user clicks empty space), the panel is auto closed, and when user clicks a widget it unhides automatically?

edit: Something I forgot to say is that when the panel is automatically opened/closed, it shouldn't move widgets around, but instead, act like an overlay.
Another thing to keep in mind is the centering feature. Currently, when right clicking (to access the centering feature), the Properties panel loses widget selection, so we'd never be able to have a centered view while showing the panel. Only left clicking on an empty space should clear a selection.