And there,almost -------in the big chair,sat her little brot

1.D
此句为倒装句型,正常句序（去除一些无关成分）为：
her little brother sat there,almost lost in the big chair
这题句子主语（即非谓语动词的逻辑主语）her little brother和非谓语动词lose之间构成如下：her little brother was lost in the big chair
此句含有固定短语be lost in,意思是“全神贯注于/沉湎于/迷失在...”.
楼主可以把这个lost理解为形容词,不必视为被动结构.
当然如果你从被动含义上考虑也可以,但是应该如下理her little brother lost himself in the big chair,而不能是：her little brother lost in the big chair.
即lose oneself in倒过来即为被动结构：sb be lost in...
2.C
同上理解,此结构为：sb expose oneself to sth,倒过来即被动为：sb be exposed to sth
所以,sb和expose之间为被动关系.
另提醒楼主两点
1）要小心动词是及物动词还是不及物动词.
这两题的lose/expose即理解为及物动词,必须加sb做其宾语,此时它们并不是不及物动词.
2）记住一些常用短语,如be lost in和be exposed to
只要句子主语和上述类似含be动词的短语构成关系,则后面短语如果做非谓语结构（比如状语）时,其答案只需要去掉be动词即可.