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.