If by responses you mean the prayers at the foot of the Altar, then yes, the Altar boy makes the responses on behalf of the Congregation.
In High Mass I think you mean the responses of “et cum Spiritu tuo”, “Amen” and the like. Yes, congregations can join in the singing of these responses and the singing of the Ordinary, where it is the norm to do so. Prayers at the foot of the altar and the like, one cannot say them in a High Mass, as the Introit is being sung at the same time.
In the Dialogue Mass one can join in with the prayers at the foot of the Altar… although I have never been to such a Mass, so I don’t know at first hand the proper procedure.