Did John fall with Mary to the right of the cross facing Jesus on Calvary?

There is nothing in scripture that says anything about this. The only reference to John with Mary the mother of Jesus at the cross was Jesus' plea to John. Jesus, dying on the cross, turned to John (the 'disciple whom Jesus loved' i.e. his best friend) to ask him to look after Mary as he would his own mother. It would have been the duty of Jesus, being the oldest son of Mary, to provide for her in this way in Jewish law. Similarly he asked Mary to accept John as her new 'son' who would look after her. We are told that from that moment John took Mary into his own home.