Hi Monica -
I think some of the confusion is coming by mixing Observation Search functionality (which allows you to filter observations by your project and view them as a distinct list of species) and Project List functionality (allows you to make a list and have it display on your project). The Project List is completely separate from Observation Search. Its just an iNaturalist List, but iNaturalist Lists do have 'taxonomic sorting' views. You can add listings to it manually and it also automatically creates listings for any research-grade observation in your project.
We made Project Lists opt-in only, so they don't display on your project unless you activate them. If you want to display the Project List on your project, click 'Display link to project list from project page' from your project's 'edit' page.
We're hoping to revisit Lists this year. There are several known problems with how iNaturalist manages listings.
Scott