This question is the two-dimensional analogue of Etale coverings of certain open subschemes in Spec O_K

There I asked if one could characterize in a way certain covers of $\textrm{Spec} \ O_K$. As Cam Mcleman answered, this is basically done by the Galois group of the maximal extension unramified outside $D$. A covering of $U$ is of the form $O_L[\frac{1}{D}]$, where $L$ is any extension of $K$.

Here I would like to ask the same question, only now for $X=\mathbf{P}^1_{\mathbf{Z}}$.

Let $D$ be a normal crossings divisor on $\mathbf{P}^1_{\mathbf{Z}}$ and let $U$ be the complement of its support.

**Q1**. Is there an "equivalence of categories" as Georges Elencwajg mentions in his answer for the analytic case. (See above link.) Basically, is there an arithmetic Grauert-Remmert theorem?

**Q2**. What is known about the etale fundamental group in this case? Is it "finitely generated"? Has anybody studied the maximal pro-p-quotients of these groups?

**Q3**. The analytic analogue would be to consider the same question for $\mathbf{P}^1_{\mathbf{C}} \times \mathbf{P}^1_{\mathbf{C}}$.

**Q4** Lars (see above link) mentions a result for $\mathbf{P}_{\mathbf{Q}}^1$. Is there something similar for $\mathbf{P}^2_{\mathbf{Q}}$?