我只分析引号内的直接引语部分。
直接引语的主干为 The valuable examples主语 exhibit及物动词 something宾语.
主语The valuable examples被which they furnish定语从句和of the power of self-help, of the power of self- help, of patient purpose, resolute working, and steadfast integrity, issuing in the formation of truly noble and manly character, issuing in the formation of truly noble and manly character 这个介词短语修饰。其中of the power of self- help, of patient purpose , resolute working，and steadfast integrity 是对of self-help的补充说明，其修饰的还是the power。issuing in = resulting in 为现在分词短语作定语修饰the power of self-help.
what it is in the power of each to accomplish for himself 为名词性疑问分句作exhibit的宾语。其中it为形式主语，to accomplish for himself为真正主语，what是to accomplish的宾语。这个疑问分句还原为陈述分句则结构如下：
It is in the power of each (person) to accomplish something for himself. 对这个陈述句中的something提问，则得到特殊疑问句：
What is it in the power of each (person) to accomplish for himself?
疑问分句用作名词性从句时需要去倒装、去问号，则得到
what it is in the power of each (person) to accomplish for himself
所以，exhibit的宾语是一个疑问分句，是不可以删去what it is in的。
