All Etale morphisms $X\to\Bbb A^1$

What are all the etale morphisms from a scheme $X$ to $\Bbb A^1_k$?

Knowing that $X\to \Bbb A^1_k$ is etale means that $X$ is $1$-dimensional I think. Additionally, $X$ must admit a zariski open cover by affines, $X=\bigcup_{i\in I} Spec(A_i)$ where each $A_i$ is a $k[t]$-algebra.

So we have that $X$ is covered by $1$-dimensional affine $k[t]$-algebras. Additionally, these $U_i=Spec(A_i)$ are taken by open immersion $U_i\to X$ into $X$, and open immersions are etale, so each of these are etale over $\Bbb A^1_k$, so we can probably simplify our analysis first to affines over $\Bbb A^1_k$.

In which case we first want to consider $Spec(A_i)\to Spec(k[t])$ morphisms that are etale. I think $A_i$ should be finitely presented as a $k[t]$-algebra, so of the form $k[t][x_1,\dots,x_n]/(f_1,\dots,f_m)$ where being $1$-dimensional means that $(f_1,\dots,f_m)$ must cut out an $n$-dimensional subvariety of $\Bbb A^{n+1}_k$.

I'm not sure if I'm correct at this point, and I'm not sure how to find all of them. I think maybe one can argue like: 1) surjective finite etale morphisms to $\Bbb A^1_k$ are necessarily just isomorphisms $\Bbb A^1_k\to \Bbb A^1_k$, 2) any etale morphism $X\to \Bbb A^1_k$ can be covered by finite etale morphisms $U_i\to X\to \Bbb A^1_k$, and composites of etale morphisms are etale 3) ???, 4) profit

Bonus: I really would like to understand all etale coverings $\{U_i\to \Bbb A^1_k\}_{i\in I}$, where the question above was my first obstruction to working this out. So any ideas on that would also be helpful.

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