Each 的指代问题

zhyanqun

OG10 的第一题：
1.The Wallerstein study indicates that even after a decade young men and women still experience some of the effects of a divorce occurring when a child.
(A)    occurring when a child
(B)    occurring when children
(C)    that occurred when a child
(D)    that occurred when they were children
(E)    that has occurred as each was a child

在OG的解释中说： Also, each was does not properly refer to men and women. 很显然 each 这里是代词，不能指代复数主语。
我想问的是以下例子, each 是什么词性？
There are four bedrooms, each with its own shower and WC. (from LDOCE)
Each 在这里是副词修饰介词结构吗？还是代词作bedrooms的同位语。

我还想请教以下例子， each是什么词性？
When the children arrive, you give them each a ballon.

多谢