(1)The old man,having worked abroad for twenty years,is on the way back to his motherland.
(2)He works in a sports center instructiing people in the use of the gym equipment.

其实我问的三个问题是一个问题。
(1)句中的having worked相当于什么？who have worked或who was having worked或其它的什么。
（2）句中的instructing相当于什么？who is instructiing 或who instructs或其他的什么。
（3）who is doing可以省略成doing,who is done可以省略成done,n那么其他类似的用法还有什么？
who do可以省略成doing吗？

句中的having worked相当于who has been working意为已经在国外工作了20年（且现在在国外仍有工作）为现在完成进行事。having worked 是将定语非谓语动词化。
分析句子成分：
The old man-------------------------作主语
having worked abroad for twenty years
-----------------------------修饰主语The old man

is----------------------------------系动词作谓语
on the way back to his motherland---作宾语成分

一个句子中只能有一个谓语，其余的动词（情态动词、助动词等不包括在内）都应该失去它的独立性，即不作谓语成分。一般都是分析该动词与修饰成分的关系，选择合适的形式。如在上个例句中，the old man与work是主谓关系，所以用主动式，再结合时态即选 having worked。如果是动宾关系，即被动式 如The British Governor arrived in Australia on January 26,today___as Australia Day
(January 26 )is (known)as Australia Day
用被动————known.



其实这都是同类问题，句中的instructing相当于who is instructiing 坐定语。至于可不可以省略要看句子有几个谓语动词，如果已有就要省略。