What are "Shtei ha'Yados"?
Rashi: They are the two thirds, who guard Sha'ar Sur and Sha'ar ha'Ratzim.
What did he command about "Kol Yotz'ei ha'Shabbos"?
Rashi: All the leaving Mishmar will be with them (Sarei ha'Me'os).
What is the meaning of "v'Shamru Es Mishmeres Beis Hashem El ha'Melech"?
Rashi: They will guard lest harm come to the king from Beis Hashem. Radak - El ha'Melech means for the sake of the king.
Malbim #1: They will guard from the outside.
Malbim #2: They will guard the Mishmeres, i.e. guards outside guards.
For how long was all this guarding needed?
Rashi: It was only the first week, until Asalyah was killed and her supporters fled the city.