I have heard the Tridentine Mass is said primarily for a homeschool group on Thursday mornings at 7:30am. It is open to the public, however it is not published as a service on the church website so I cannot say if it will reliably be happening every week. All the parish Masses otherwise are according to the Ordinariate Use missal, Divine Worship.
Mass is said in English. However, many parts are done in Latin on a semi regular basis such as kyrie, agnus dei, sanctus & pater noster. As far as English mass goes, Incarnation is the most reverent church around.
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