This being the case这个短语结构看不懂，意思为什么是在这种情况下？

Question

this is a matter over which we can exercise no control.这里的over是什么成分什么词性什么意思？which引导定语从句？no control又是什么成分？
We are very grateful to his for what his has done for us.这句话有错误吗？为什么是to his？
We hope they will reach you in due course and will help you in making your selection .这里will help you in making your selection这句话符合语法吗？我看不懂
We are in receipt of your letter dated Aug 10.这句话句子结构成分看不懂？

Answer 1

1This being the case这个短语是现在分词being的独立主格结构 作状语
所谓分词独立主格结构 就是分词自带逻辑主语构成。
This是being the case的逻辑主语。意思是 这就是那种情况。可以翻译成 在这种情况下。
现在分词作状语 如果其逻辑主语 与句子主语不一致，现在分词可以自带逻辑主语 构成独立主格结构
如 his mother being ill，he had to look after her.
2this is a matter over which we can exercise no control.这里的over是介词 有 关于的意思

over which是带介词的关系代词 引导定语从句 。no control是名词作定从中的宾语
定从意思是 we can exercise no control over the matter
句子意思 我方对此事实属无能为力
3We are very grateful to his for what his has done for us.这句话有错误
应该是We are very grateful to him for what he has done for us.
4We hope they will reach you in due course and will help you in making your selection .这里will help you in making your selection这句话符合语法
you是宾语 in making your selection可以看做介词短语作状语
其中 making your selection是动名词短语作介词in的宾语
其中your selection是动名词making 的宾语
句子意思 将 在做出选择方面 帮助你
5 We are in receipt of your letter dated Aug 10.这句话句子结构成分

We 是主语are是系动词 in receipt of your letter是表语
dated Aug 10.是过去分词短语作定语修饰your letter
句子意思 我们收到你8月10号的来信来自：求助得到的回答