This sounds like it would be frustrating. How I would go about my workflow is to first unpublish the module and items. Then I would publish the individual items that I wanted before publishing only the module.
You could do that in reverse order if you wanted. Unpublish all and then publish only the module, then go in an publish each item within the module.
In terms of the announcements, to delete an announcement then click the ⁝ kebab icon to the right and delete. If it's an announcement that you want to post later in the course (such as a midterm check-in) then open the announcement, click edit, and at the bottom check "Delay posting" and put in the date and time you want it to appear. I often schedule many announcements before the class begins.
