>How similar are modern Icelandic and Faeroese, particularly in terms of
>phonetics? Which is closer to Old Norse?

I see Óskar is already writing an answer to this,
I'd just like to point out one thing.

Old Norse had nasal vowels (as French does) but they were not marked
in writing so we don't know where they were. No descendant of ON has
preserved those nasals. This is one of the things that make it impossible
for us to obtain a precise reconstructed pronunciation of the language.

It is, for example, quite possible that the ó in Þórr was a nasal vowel.

Regards,
Haukur