$X$ is smooth since $f$ is étale and simply connected, since $X$ is $\mathbb P^1$ or $\mathbb A^1$. Every map $\mathbb P^1 \to \mathbb A^1$ is constant hence not étale. Every map $\mathbb A^1 \to \mathbb A^1$ is given by a polynomial, hence finite unless it's constant, and again constant maps are not étale.

$X$ is smooth since $f$ is étale and simply connected, so $X$ is $\mathbb P^1$ or $\mathbb A^1$. Every map $\mathbb P^1 \to \mathbb A^1$ is constant hence not étale. Every map $\mathbb A^1 \to \mathbb A^1$ is given by a polynomial, hence finite unless it's constant, and again constant maps are not étale.