From the given options, which sentence/sentences is/are grammatically…

The correct answer is Option (1) → (B), (C) and (E) Only

Prepositions in "wh-" questions:

• A preposition that goes with the question word can stand in one of two places:
  • At the end (everyday English): "What are you looking at?"
  • At the front, before the question word (formal English): "At what are you looking?"
• The preposition is used only once. Putting it both at the front and at the end repeats it, and the question becomes incorrect.
  Example: To whom did you give the keys?

(A) What are you looking at? — Correct.

• The preposition at comes once, at the end.

(B) At what are you looking at? — Incorrect.

• At is used twice, before "what" and again at the end.
• Correct form: What are you looking at?

(C) About what are you reading about? — Incorrect.

• About is used twice.
• Correct form: What are you reading about?

(D) What are you reading about? — Correct.

• The preposition about comes once, at the end.

(E) For whom are you searching for? — Incorrect.

• For is used twice.
• It should be "For whom are you searching?" or "Whom are you searching for?"
• Correct form: Whom are you searching for?