I will keep you updated the orders situation we booked这句话看不懂

0.I 是主语will keep 是谓语you 是宾语updated是宾补 the orders situation保留的updated的宾语 we booked是定语
我们将为您提供我们最新的订货情况.
1We suppose this mistake might have been made in the packing through the confusion of numbers.这里的介词through是 在…之间;在…之中 的意思
2We apologize for the trouble caused to you by the error,and will make every effort not to let such a mistake happen again.
这里the trouble caused to you by the error是介词for的宾语
其中caused to you by the error是过去分词短语作定语 修饰the trouble
其中to you 是状语修饰caused.by the error也是状语修饰caused.
意思是 由于错误给你造成的麻烦
3Please do your utmost to expedite same,so that we may execute the order smoothly.这里的same的意思 是 该事
（法律、商业文书用语中常省略the）该人,该事
4I am sorry to say that the goods you ordered on 25th June are among those held up.
这里的among those held up的意思 是 在那些被停运的货物中
5Meanwhile,we apologize for the delay and hope you will understand that it is due entirely to cause outside our control.这里it is due entirely to cause outside our control.的due
即 due to 中间插入了 作状语的副词entirely
cause在这里是名词
outside our control.是介词短语修饰cause

through在这里可以当成中文的“由于”理解（Because of; on account of）

由于此失误给贵方所造成的麻烦

与原定单相同的货物

在这些（被暂扣）货物之中

cause在这里不是动词，是名词，“原因”的意思：这完全是由于我们无法控制的原因所造成的...