Repeating as a partial answer:
As to the last point, found this:
Simbiology / Preferences / Indicators
Show indicator when a block is pinned checkbox.
Note that when this box is unchecked, the pinning icon is automagically turned off for most but not all, SimBiology graphical constructs. Labels are still shown as pinned. To turn those icons off, I unchecked the box in preferences and then unpinned and repinned. This seemed to work. I suspect that saving and reopening the model would work, too.