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The familiares of a bishop or cardinal wear ferraioli over cassocks not usual choir dress (surplices). I suspect this is because the familiares are more like personal attendants of the prelate rather than strictly liturgical ministers.
The role of the familiares is to assist the bishop with vesting at the altar and handle items like the miter, crozier, etc.
The man with the red hat is a page carrying the galero of the Cardinal. The galeri are not usually worn in liturgy, but are sometimes carried as a symbol of the office of the Cardinal. I don't recall specific rubrics around how he dresses, but especially given this is the Institute of Christ the King, the more archaic dress style seems appropriate.