He placed the breastpiece on him

"Moses placed the breastpiece on Aaron"

the breastpiece ... the turban ... the golden plate, the holy crown

These are all special garments that Yahweh commanded the people to make for the priests. (See: rc://en/ta/man/translate/figs-explicit)

It is not clear what these are. They were objects that the priest somehow used to determine the will of God. (See: rc://en/ta/man/translate/translate-unknown)

a man's head covering that is a long piece of cloth wrapped around the head

These two phrases refer to the same thing. It was a plate of pure gold attached to the turban.