Hi, Laurel!

> There must be some reason why it is "hann heiti" in the first part of the phrase and "hann heita" in the second part, but I don't know what it is, or if there should be some nuance in translation. I just made it "be called" each time.

The first is subjunctive, the second is indicative.
There are many ways of looking at it. One very down-to-earth
approach is to remember that "vilja at" is one of the
phrases that triggers the subjunctive.

Hann vill fara.
Hann vill at hon fari.

Come to think of it, doesn't it work like that in
English as well?

This is correct:

He insisteth that she go.

But this isn't:

*He insists that she goeth.

> Also, in Hrafnkel we had varying forms of "heita" used with place names. These were sometimes prefaced with "í" and sometimes with "á". Why the preposition, and why two different ones?

I wish I had a better English example but let's
imagine that there is a functional relationship
between place names and prepositions so that,
for example, you'd always say:

He's IN London.

but you'd also always say:

He's AT York.

so that

*He's AT London.

and

*He's IN York.

were not allowed.

That's sort of how things work in Icelandic.
For example Hafnarfjörður and Raufarhöfn are two
municipalities. One takes 'í' and the other 'á'.

í Hafnarfirði
á Raufarhöfn

You can't possibly say:

*á Hafnarfirði
*í Raufarhöfn

So you should just be grateful when the appropriate
preposition is given with the name :)

Kveðja,
Haukur