Once students have joined your section, you will be able to view their progress by-puzzle, in all courses. You can conduct student grading by seeing how far they've progressed in a course, and to what degree of accuracy they've completed all puzzles.
From your list of sections at your teacher homepage (https://studio.code.org/home), just click on one of the section's names in the far left column to be brought to the progress view for that section.
On that progress view, you'll see a list of all student names on the left, and a grid on the right showing progress bars that fill up vertically (top to bottom), indicating progress made in a given lesson.
You can click on a student's name to see a more detailed view for their progress in a given course, down to each level (each indicated by a colored bubble).
Note that the assigned course for a given section is just the first one students will be brought to once they sign in each time. Students will have access to all courses at all times, and you can click the dropdown list next to "View progress in: " for changing the course for which you're viewing progress in. This is highlighted above in a red square. There's no need to make new sections or move students around just for a different course assignment.
Viewing Submitted Work
In addition to viewing how far students have progress in a given course, you can view their submitted work in any puzzle. This can be done by clicking one of the bubbles shown in the image above, or by visiting a puzzle directly, such as at https://studio.code.org/s/20-hour/stage/5/puzzle/2.
Click the blue arrow on the right side to bring up the teacher panel, where you'll see dropdown options for selecting a section, then another list for selecting students within that section. Choose a student to see their submitted work for that puzzle.