o answer your question specifically: Your code already shows that you are using SessionState.
Therefore in your DisplayQuestion() method I would implement a check against the current question Retrieved from the session and update the checkboxes checked state accordingly.
When your survey starts you add the questionnaire to session
When a page loads you retrieve the current question and response from the session state
Update the checkboxes checked state if the user has previously answered the question.
When the user proceeds to the next question update the users response in session.