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Quantifier Equivalences

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Prenex normal form question right?

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Logic - Translate a Math Statement

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Does the placement of the quantifier make any difference in the following examples.

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Is this argument correct?

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Why is $\forall x \in A:P(x)$ equivalent to $\forall x (x\in A \to P(x)) $?

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$(∀x)(∃y)(x>y)$ is false. But then why is $ (∀x)(∃y)(x\geq y)$ true?

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How can I write one-to-one and onto in predicate logic?

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