When I hold down the spacebar (to get the Hand tool) and try moving my view over to the left or up, I can't go past the left of the Stage or the top of the Stage. Why is that?
Most likely the View, Work Area menu item isn't selected (that is, it doesn't have a check mark next to it). Only when this is selected can you (the author) see outside the Stage. (I recommend leaving this setting in the default, selected state.)
I swear my Properties panel used to be taller. What did I do to get the "slim view"?
The Properties panel has a special "info area" that can be hidden via a tiny arrow button at the bottom right. You can also trigger that button by double-clicking in any blank area of the Properties panel. Just click that arrow button to restore the Properties panel's full view.