That "brown metal part" is the EGR valve. Coolant is not leaking from it. Coolant is spraying there from a leak nearby, then you see it dripping down from there, like in this picture.
It's a plastic part or a gasket. Did you use Motorcraft, or Dorman? You say you changed them all, but it sure looks like 2W9Z-9N499-AC is not new. There's a lot of dried coolant residue on it. It's also possible that you twisted the big o-ring seal between it and the crossover tube. It's easy to do.