To download students' grades, click on Gradebook and then click the Download button in the upper-right corner of the page. This will download the gradebook as a spreadsheet.
To download students' comments, navigate to the Assignments tab on the course home page, and select an assignment. Then click on All Comments and click the Download button at the bottom of the resulting window.
To download all comments by a particular student across the entire course, navigate to the Students tab on the course home page, and select a student. Then click on Download all annotations.