with结构的理解

with的理解就是，

它是个“阑尾”，要可以， 不要也行。

有时候，没有这个with, 会觉得句子不平衡，

有时候，有这个with，会觉得多余，做作。

这样说，就像我们写汉语作文时的心情：如何感觉是好？--- 那就看你个人的文采了。

英文的文采除措辞、表达、篇章、哲理等等之外，还有一个结构问题，这也算。

结构上是这样的，

He came in, and a book was in his hand.

1. He came in, a book being in his hand. (这个being明显多余)

2. He came in, a book in his hand. （√）

3. He came in, with a book in his hand. （√）

如果有人感觉得出2不是太爽，就加个with变成3. 

2与3的区别，2稍正式，3更趋向口语化一点（实际口语也不太可能出现这种语体）。

比如更正式的，

4. He came in, book in hand. 

别问book前为何没有冠词，有些就是要“裸奔”的，如 

Boy though he was, he embroiders very well.

I have no such book.

### in hand是固定词组，hand前自然不用冠词。

所以

1. He died with his dream unfulfilled.

它的原始句是：He died, and (或so) his dream was unfulfilled.

也可以是，He died，his dream unfulfilled.

2-3略

补充一句写作：

Sarah sank in the nearest chair. She was completely exhausted, her limbs were stiff with cold，and her mind was a piece of blank 

---> Sarah sank in the nearest chair, completely exhausted, her limbs stiff with cold ，and her mind a piece of blank. (注意两个标红的and性质其实不同)

举这个例子的意思是，加 with 是保险的，不加未必能做到恰如其分地好。

再小改一下，把句子弄平衡一点：

With her limbs stiff with cold,（and）her mind a piece of blank, Sarah sank in the nearest chair, completely exhausted.

你的问题：

(1)和(2)中,unfulfilled和growing well  这些能看作后置定语吗?但看着和分词的独立主格用法也很像?

--- 你觉得还要管它们叫什么吗？

含混一点，叫名词后的修饰语吧；准确点，则是“with这个介词的宾语的补足语”

(3)句第二个with指的是child冷,还是hands冷啊?

--- with hands red with cold. 

原始句是，and his/her hands were red with cold. 自然是指手被冻红了。