lost 用法

老师您好：
1 ____ in thought, he almost ran into the car in front of him.
A. Losing B.Having lost C. Lost D. To lose (96高考 23题)
答案给的是C，有的老师说是过去分词，有的说是形容词。在 赵振全 的《英汉常见问题解答大辞典》中解释为形容词。我很迷惑，到底是lost到底是什么词，在句子中做什么成分。
2_____ in the mountains for a week, the two students were finally saved by the local police.
a. having lost b. lost c. being lost d. losing
（江苏2005 27题）
此题答案是B， 这个又怎么解释？
我实在是搞不清了，麻烦老师了！