I'm looking for the simplest way to have two activities displayed at once, so that one Activity always remains visible, and the other changes with user interaction.
In other words:
I've seen many different ideas for doing something similar, but haven't been able to adapt them to my needs.
Any help would be appreciated.
None of what you want is possible with activities. The closest thing is using themes so that your "side activity" is partially visible behind other non-full-screen activities. However, getting this to work properly on a wide range of screen sizes will be difficult, and managing your task stack to pull this off does not strike me as being much fun.
You should be able to create something that resembles what you seek with the proper application of fragments, but you will wind up with one large activity and a bunch of fragments, as opposed to a bunch of activities.
At the activity level, Android is not designed for some persistent element that you seek.