C宾语从句,of后跟了句由what引导的宾从,what是代词,指带了事情.
B定语从句,whose是定语,在这指物（那棵树的树枝）,去点中间那部分That tree is very old.是一句完整的句子,定语从句就是起修饰作用,在这修饰先行词tree那棵树.
D第三句:想要避免掉人类所有容易犯的愚昧无知,是不需要超级天才（出世）的.
这个句子的主语是后面的superhuman genius超级天才.句首的to ,是in order to（为了） 的略语,整个句子是倒过来了,我现在把它还原过来：
No superhuman genius is required in order to avoid the various foolish opinions to which mankind is prone.
is required,被需要,被动语态.
接着,从句里面的to which mankind is prone,原本的to也可以放在prone的后面的,be prone to（倾向于）.修饰前面的foolish opinions.
现在比较一二题,
第一句是宾语从句,从句为what was going to happen,去掉以后发现主句不完整
I had not event a vague idea of,缺少的是宾语.
第二句是定语从句,从句为Whose branches are almost bare ,去掉以后发现主句是完整的That tree is very old.
关键：断句,看主句是否完整.