Hi Chris,
I had all of these questions a couple of years ago and it's been a slow process to find the answers. Here's what I've found by trial and error:
-There are some places that seem to come from Yahoo's geoplanet that are not editable and only have a point location. The only way to get rid of them right now (even for curators) is to email an admin.
-Projects only show up in a place if that place is defined as the boundary for the project. There is no geographic algorithm that automatically assigns projects to places.
-If a place has a project and you merge it with another place, the project is moved to the merged place. Also, if you rename or otherwise edit the place, the project remain attached to the place because they are linked by the place_id number, not the name.
-At one time, someone, somewhere post url modifiers that let you search for places by their parent place id. I can't find the post or the modifiers now and I'm kicking myself for not quadruple bookmarking that page.
-All of the data you're asking for exist in the database that runs iNat but access to those data are extremely difficult.
People have been asking for improvements to the Places for years but it's clearly a low priority. For many of us who use iNaturalist as part of our jobs, Places are very important, more so than the AI for identifying common species.