What is the significance of these figures in a Catholic ordination procession?

In this video by the Institute of Christ the King Sovereign Priest, we can see brief moments of the procession into the church. At the front of the procession with the cardinal (at 5:04), there appears to be a man dressed in archaic *secular* clothes holding a red hat. It seems obvious this is related to the dignity of a cardinal, but why is he dressed that way? Right behind him are two clerics who appear to be wearing ferraioli . The ferraiolo is also seen at other places, why might a priest wear this instead of choir dress ? Lastly, in the same video we see at minute 2:58, a man wearing, again, archaic secular dress wielding a pike. Why is he there?