genius

  1. People described him as a genius.
    1a. People described him as being a genius.
  2. People described him to be a genius.
    2a. People described him to be as a genius.
    Please correct all.
    Thanks.

2a is incorrect.

You might say ‘People said he was like a genius’. This is not the same as the others which indicate that he is seen to be a genius, rather than he is seen to be genius-like in some way.

Beeesneees,
Can I write : “People described him a genius.”?
Is it right or wrong?

That is incorrect - it would have to be something like “People described him as a genius.”

Beeesneees,

  1. He is an ingenious man.
  2. He is a genius man.
  3. He is a genius.
    Please correct all and comment.
    Thanks.

2 is incorrect.
1 and 3 do not mean the same.

Beeesneees,

  1. He was a child(n/adj) genius(n).
  2. He is a genius(n/adj) man(n).
    When #1 is OK, Why not #2 OK?
    Here both ‘child’ and ‘genius’ are nouns.
    Please explain the grammar points to understand.
    Thanks.

Those sentences have different structures, as indicated yourself!
In the first ‘genius’ is a noun. In the second, it is an adjective.

In ‘he is a child genius’, ‘child’ equates to ‘adult’.
He is an adult genius
is okay grammatically, but logically you don’t need to point that out!