One has big problems trying to make category $B$ work. Standard Lefschetz principle arguments justify Lars' use of $\mathbb C$ even if $k$ is not, in fact $\mathbb C$. Thus, we can write $A$ as the category of representations of $\pi_1^{top} \to GL_n (\mathbb C) $ Any $l$-adic construction is going to be about continuous representations $\pi_1^{et} \to GL_n(\mathbb C)$ for some topology on $GL_n(\mathbb C)$. To get an equivalence of categories in any kind of nice way, we clearly need every representation $\pi_1^{top} \to GL_n(\mathbb C)$ to extend to a continuous representation of $\pi_1^{et}$. So its image must lie in a compact subgroup. But $GL_n(\mathbb Q_l)$ has elements, like $\frac{1}{l} I $, that do not lie in any compact subgroup. I don't see any way to modify this construction to fix that bug. For 3), you may find <a href="https://mathoverflow.net/questions/123857/how-to-see-the-geometry-and-arithmetic-of-tannakian-fundamental-groups/123882#123882">my answer here</a> interesting.