Smooth, unramified, and etale morphisms are stable under base change, so $Y\times_X Z \to Z$ is {smooth, unramified, etale} if $Y\to X$ is {smooth, unramified, etale}.

Either you misread the exercise and it's asking what I'm asking or what Qing Liu is asking, or there is a mistake in the book.

Smooth, unramified, and etale morphisms are stable under base change, so $Y\times_X Z \to Z$ is {smooth, unramified, etale} if $Y\to X$ is {smooth, unramified, etale}.

Smooth, unramified, and etale morphisms are stable under base change, so $Y\times_X Z$ is {smooth, unramified, etale} over $Z$ if $Y\to X$ is {smooth, unramified, etale}.

Either you misread the exercise and it's asking what I'm asking or what Qing Liu is asking, or there is a mistake in the book.

Smooth, unramified, and etale morphisms are stable under base change, so $Y\times_X Z \to Z$ is {smooth, unramified, etale} if $Y\to X$ is {smooth, unramified, etale}.

Either you misread the exercise and it's asking what I'm asking or what Qing Liu is asking, or there is a mistake in the book.