Is “Analytics” a plural or singular noun?

Analytics is an uncountable nous. Which of these sentences is INCORRECT?

Analytics is crucial for understanding customer behavior.

Analytics are crucial for understanding customer behavior.

Which of these sentences is INCORRECT in using “analytics” as a noun, adjective or adverb? 

Analytics is essential for data-driven decision making.

Analytical skills are highly valued in the industry.

Is it correct to say: “John is very analytical and often examines every detail before making a decision”?

Yes, “analytical” is an adjective in this sentence.

No, it should be “John is very analytically…”

Is this sentence correct: “He has an analytically mind”?

Yes, “analytically” is an adverb in the sentence

No, it should be “He has an analytical mind”

Is this sentence correct: “She analytically examined the report thoroughly”?

Yes, “analytically” is an adverb in the sentence.