Is there a way to edit all of a ticket's fields on one page?

Yes, the "Edit Ticket" page shows the ticket's fields in one form: subject and message, requester, "Status", "Priority", "Group", "Assign", "Tag" and all custom fields, plus an "Add field" button to attach more fields. Make your changes and click "Update Ticket" to save everything at once. For quick single-field changes, editing directly in the ticket sidebar is usually faster.