1------by the snake,the little girl crying loudly.

1.后句中漏了be 动词,is 或 was crying loudly.
Frightened by the snake 作为状语,形容的是主语 the little girl,并表达了因果关系,说明后句中为何 (is/was) crying loudly.
整句的意思连贯起来就是：
（因为）被蛇（的模样）吓了一跳,小女孩哭得很大声.
2.I hurried 表示了现在陈述的是过去发生的一件事,赶到机场之后发现我原本要搭乘的飞机“已经起飞了”
这个“已经”发生的时间比“我赶到机场”更早,所以用过去完成时 had taken off.
it's "the plane" that had taken off,从句中,the plane 是主语,I wanted to take 补语,had taken off 谓语.

1------by the snake，the little girl crying loudly。
填Frightened，请解释
小女孩the little girl 和 frightened 之间是被动的关系，小女孩被惊吓，所以用frighten的过去分词形式，表示被动语态
2I hurried to the airport only to find the pla...

had taken off是固定短语