Hi hmosiejones,
For the first issue that you couldn't get the down arrow under status, the status shows the project's progress. When user uploads the document on the SharePoint Online, the down arrow beside Status column will appear.
For the second issue that how they go in and mark as approved. Please confirm if the Admin has permission to access SharePoint Online.
Based on the situation, if the Admin has permission to access SharePoint Online. Please refer to the following steps.
1. Admin need login the SharePoint Online site.
2. Go to Task list which you choose to keep track of work when you create workflow.
3. Click the document which needs to be approved.
4. Click Approve.
Thanks,
Ida Qiu