1. 这两个的区别是过去分词作原因状语通常不强调和谓语动词的动作同时发生的意味，一般是分词动作在先，主句产生的结果在后。现在分词经常强调正在进行的动作，但在有的语境中，可与过去分词作状语同义。

Being written in haste, the composition is full of mistakes. 这是出自中国语法书上的句子，很多外国人是不认同的，因为being written 表示书还在写作中，全句就不太合乎逻辑了。请看国外两个语法论坛对这句话的讨论：

WR: It’s not a good sentence. Presumably written is meant as an adjective, but it doesn’t come across that way. That use of being tends to imply that the composition might still be in the process of being written.

Being written in haste, the composition is full of mistakes.  ​(bad)

Having been written in haste, the composition is full of mistakes. (good)​

The composition, [which was] written in haste, is full of mistakes. (good)

https://forum.wordreference.com/threads/being-written-in-haste%EF%BC%8Cthe-composition-is-full-of-mistakes.3622797/

Grammar Exchange:

I share Gustavo's view that the perfective construction ("Having been written in haste") is much better, even if Chinese grammarians don't hear it as being better. Here is a sentence in which "being written in haste" would work.

Being written in haste, the composition will doubtless be full of mistakes.

Notice that the sentence refers to something that is being written rather than to something that has already been written. 

https://thegrammarexchange.infopop.cc/topic/being-written-in-haste-the-composition-is-full-of-mistakes-from-a-grammar

2. as 在这里可以理解为：作为