hardly anyone believes that today

正确，只是hardly是修饰的anyone，句子的主语，所以这句子没倒装。
hardly作状语，修饰动词的时候，句子才要倒装。

正确的。
原句应该是这样
There is hardly anyone who believes that today.

正确
不是倒装
nearly nobody believes that today

是正确的， 正语序是：
Anyone hardly believes that today!

Anyone hardly blieves that today.
今天几乎没有人相信。

当然正确，今天几乎已经没人相信它了