这么多啊，吓死人了。后面的我几乎没有弄了，就是复制资料了。

‍‍　　根据你提供的例句，你所归的类有些问题。这里应该包括以下几个方面：

　　1、“there being + 逻辑主语”构成的的分词独立主格结构。

　　复立主格结构的一般形式是“逻辑主语 + 分词”。由于 there be 的主语在后，因此就成了“there being + 逻辑主语”这种特殊形式。分词的独立主格结构可以用作时间状语、原因状语、条件状语、伴随方式状语，there being 也不例外，如：

　　There being nobody in the room, the light is always turned off. 屋里没有人的时候，等总是关着。（时间状语，= when there is nobody in the room,）
　　There having been no rain, the ground was dry. 由于没有下雨，所以地面很干。（原因状语，= because there had been no rain）
　　There being enough time, we would do it better. 如果时间充足，我们会做得更好。（条件状语，= if there is enough time）

　　2、“there being + 逻辑主语”也可以是动名词的复合结构。

　　动名词具有名词的语法功能，可以作介词of、about、on 的宾语

　　There is now some hope of there being a settlement of the dispute. 现在有点希望可以解决这次争端。（原例句）
　　They disputed with us about there being some chance to quiet down the disturbance. 他们与我们争论存在平息这次事端的可能性。
　　They planned on there being another meeting. 他们打算再开一次会。（原例句）
　　I would come except there being rains. 要是不下雨, 我就来。

　　3、不定式短语“there to be”

　　不定式具有名词性、形容词和副词性

　　1）名词性（常用作意念动词like, prefer, hate, want, mean, intend, expect, consider以及let构成的祈使句和介词for的宾语）

　　I don't mean there to be any unpleasantness. 我无心引起任何不愉快。 （动词mean的宾语，= that there can be any unpleasantness）
　　I don't want there to be any misunderstanding. 我可不希望有任何误解。（动词want的宾语，= that there will be any misunderstanding.
　　Students hate there to be too much homework. 学生讨厌做太多的家庭作业。
　　It was too late for there to be any buses. 太晚了，不会有公共汽车了。（= for there can be any buses）
　　They asked for there to be another meeting. 他们要求再开一次会议。（= asked for there could be another meeting）

　　2）形容词性（用作后置定语和宾语补足语）

　　I don’t hope any mistake there to be about it. 我不希望对此事存在任何误解。（there to be about it 是mistake 的后置定语，= mistake which there will be about it）
　　Let there be no mistake about it. 不要误解我的意思。（there 是宾语，be no mistake about it是宾补，= let it no mistake about it there to be）

　　3）副词性（目的或结果状语）

　　I will try my best to do it in order there to be fewer mistakes. 为了少出些错误，我会尽力的办的。（目的状语，= in order that there will be fewer mistakes.）
　　I paid so much money as there to be no much left. 我画出大量的钱以至于所剩无几。（结果状语，= so that there was no much left）

【你的篇幅太大，归纳又不太系统，整理起来很费劲，也可能遗漏了不少。以后是否可以把问题划分的小一些分开提问？】