I've now seen some negative comments about a few points in Kiernan.

But it appears that the linear independence was made more nearly explicit by Dedekind (see p.7 of hss.cmu.edu/philosophy/techreports/184_Dean.pdf) in his Vorlesungen. That article also credits Artin with the formulation of the Fundamental Theorem in abstract terms, while crediting Dedekind with the theory for subfields of the complex numbers.

There do seem to be books. One of my "issues" is this: do the historians of Galois theory "read back" what the scope of the theory is supposed to be, from the way it looked in say 1950? The explicit cases of elliptic curve isogenies of multiplication by n, and maybe coverings of modular curves, were well known to Weber (another answer). We know about "Galois theory of coverings" now: how did it look then?

In Whittaker and Watson, end of the Gamma function chapter, by the way.

The question "U(3) Sato-Tate measure" is a quite different example.

Who proved the normal basis theorem?

One value of p at a time, or for a range of p? It seems to make quite a difference.

I assumed this calculation of the Jacobian determinant of F was accessible to computer algebra packages (I don't have access to one). Three of the entries in the determinant are zero, and there is some simplification evident by hand. I had no time last night to work on this.

Is this question well-posed as it stands? The embedding per Q2 controls much more of the geometry, it seems, than the abstract Cayley graph, which may just be some tree (for a free group). For example at en.wikipedia.org/wiki/Fuchsian_group#Limit_sets you can read about a large class of Cantor sets, but these are associated to a definite group action, not an abstract group.