To remove an Announcement, go to Announcements (on the left menu) and check the box on the right side on the same line as the announcements you want to remove. The boxes are under the column headed Remove. Then click Update at the bottom of the page.
To avoid having Assignment announcements, don't check the Announce the Open Date box when you create the Assignment.
You cannot change the order of announcements. They are listed chronologically, with the most recent first.
2/21/06