1. With the help of the firemen,they were able to leave the burning house.  (With the help of the firemen 表示条件? 原因?)

——方式状语。也可分析为原因。

2. I had a quarrel with my father about some trifles.  (with my father about some trifles 整段作 quarrel 的定语吗?)

——方式状语。也可分析为 quarrel 的定语。

3. The explosion was timed to be simultaneous with the plane's take off.  (这里的with不太理解,它是主语的补充吗?)

——时间状语。“在飞机起飞时 / 随着飞机的起飞”。