1)
Why did he write them?
1.
'Rashi': It is for a remembrance of the order.
2.
Radak: He wrote them on 24 pieces of parchment, to cast a lottery.
2)
What do we learn from "Echad Achuz l'Elazar Achuz Achuz l'Itamar"?
1.
Malbim, from Ta'anis 27a: The first 16 Mishmaros were the previous ones. The eight added were all from Elazar - as much as they had before. Itamar remained with the eight that they had initially.


