There's no compensation if your leisurely overnight in BRU is screwed up by a flight delay on FCO-BRU. Final destination is all that matters for that.

If UA merely cancels EWR-CHS, they should indeed be liable for EC261 compensation, but I doubt that they will pay willingly.

If BRU-JFK arrives so late that you miss the flight from EWR, then SN would be liable. They also might not be too willing, but it's at least more of an open-and-shut case.

All airlines involved will claim "extraordinary circumstances" if customs, Uber, traffic, etc. cause you to miss your flight from EWR even though the flights had minor delays.