I have custom fields on my Submit a Request form that I would like to display in the table shown to my end users via the My activities option in the Help Center. Is it possible to include a custom field as a column on this table?
Yes, you can display custom ticket fields to end-user within the portal using the new request list experience. You can see the announcement of this new feature here.
For more information on getting started with the Open Beta, see the article: Using the new request list experience in the help center customer portal (Beta).