Unfortunately, the customization of most list items is pretty limited at this point. I think a lot of your thoughts and use-cases are related to this previous thread: More patient data messages and people tab (which also contains an overall summary of what customizations the CHT does support).
From a general workflow perspective, I think a typical approach to handing #1 and #2 is via tasks (which do have some limited customization and prioritization).
I have not done any tinkering with this, but regarding #3, I wonder if it might be possible to leverage the UHC Mode. In theory, that could show who was screened. (I think the main issue with this would be that it is currently hardcoded to a monthly interval (so it only cares about visits in the last month), which might not fit with your usecase.)