1、having done 是非谓语动词中现在分词的完成式。与现在分词一般式doing 相比,doing表示的动作或状态往往与句子谓语动词表示的动作或状态同时发生,而having done 强调在谓语动词之前发生,即已经是完成时。having done 通常在句中作状语,表示句子主语发生的动作或存在的状态,与主语是主动关系。例句:①Having worked there for 30 years, Haydn moved to London.②Having promised to stay with my mother, I didn’t accept the invitation to the party
having been done, 与句子主语之间是被动关系。例句:Having been discussed for many times, the problem remained unsolved.该句同样可变为:Although it had been discussed for many times, the problem remained unsolved
2、being done
一、与be动词一起构成现在进行时的被动语态（am/ is/ are being done）和过去进行时的被动语态（was/ were being done）。如：
The new houses are being painted.这些新房子还在刷漆。
When I went to pay him a visit, he was being examined by a doctor. 当我去看他时，他正在接受医生的检查。
二、作后置定语，修饰某一名词，表示某一被动动作正在进行。如：
The meeting being held now is of great importance. 现在正在开的会很重要。
上面的句子也可以变成含有定语从句的句子：
The meeting which is being held now is of great importance.
注意：being done，to be done与done均可作后置定语，其区别为：being done表示正在发生的被动动作；to be done表示将要发生的被动动作；而done表示已经发生的被动动作。如：
The house to be built here next year belongs to Fred. 明年将在这里建的房屋是弗雷德的。
The house built here last year belongs to Fred. 去年在这里建的房屋是弗雷德的。
三、作某些及物动词或介词的宾语。如：
John hates being laughed at in public. 约翰不喜欢当众被嘲笑。
Do you mind being left alone at home. 把你一个人留在家里你介意吗？
My class teacher was honoured for being devoted to the cause of the education. 我的班主任因致力于教育事业受到了表彰。
四、有时作主语或用在see，hear，feel等少量感官动词后作宾语补足语。如：
Being lost can be a terrifying experience.迷路可能是一种可怕的经历。（作主语）
He heard the song being sung next door. 他听到隔壁有人在唱这首歌。（作宾补）
参考了
http://res.tongyi.com/resources/old_article/student/217.html追问having been done与being done。 having done与not having done分别举一下例子，并标注汉语