Are all principal $\mathbb{G}_a$-bundles trivial?

Question

I am considering the group scheme $\mathbb{G}_a:=\mathrm{Spec}(\mathbb{Z}[x])$, the additive group.

I happen to know that the classifying space for $(\mathbb{R},+)$ is a singleton, which means topologically every principal $\mathbb{R}$-bundle is trivial. Then I want to know about the algebro-geometric analogue.

My questions are:

1. Are all principal $\mathbb{G}_a$-bundles trivial? Or what is the stack $[*/\mathbb{G}_a]$?
2. If the answer is negative, can you give an example of non-trivial principal $\mathbb{G}_a$-bundle?
3. If we ask for $\mathbb{G}_a\times S$ for a scheme $S$, do answers change?

Answer 1

Let $$ X = (\mathbb{P}^1 \times \mathbb{P}^1) \setminus \Delta, $$ where $\Delta$ is the diagonal. Then the projection $X \to \mathbb{P}^1$ is a nontrivial principal $\mathbb{G}_a$-bundle.