Choose the sentence with the correct determiner.

The correct answer is Option (1) → Do you have any information about the lost child?

Any is the determiner used in questions and negative sentences with uncountable nouns and plural nouns. "Information" is uncountable, so "any information" is correct in this question.
Example: Is there any milk left in the fridge?

Why the Other Options are Incorrect?

Option 2: How few sugar did you buy? — Incorrect. "Few" goes with countable plural nouns; sugar is uncountable, so the question needs much.
Corrected: How much sugar did you buy?

Option 3: The head is the much sensitive part of the body. — Incorrect. "The" before a comparison of one thing with all others needs the superlative, "the most sensitive".
Corrected: The head is the most sensitive part of the body.

Option 4: He had absolutely a few knowledge about the postponement of the examination. — Incorrect. "A few" is for countable nouns; knowledge is uncountable. The sense "almost none" needs "little".
Corrected: He had very little knowledge about the postponement of the examination.