>How can one claim to know 13th century Icelandic?

We can certainly make an educated guess.
Even when the scribes write as archaically
as they can they sometimes give themselves
away :) Much as when I write exercises for
the Norse Course - every now and then an
"og" slips in instead of "ok".

>Much of what was
>written during and before that period, especially those texts that
>has remained for the future, was influenced by a sort of arcaism
>tendence.

Quite true.

>What sounded older also sounded better.

Well put. Although, in most cultures there is
a certain conflict between the traditional native
style and a newer (often foreign, or thought to
be foreign) style.

>I had made the
>assumption that texts dated to a certain time in history always
>reflected the language of the preceeding century, when it comes to
>Old Norrse.

That's a very interesting rule of thumb :)
You could indeed say that the spelling lags
behind the actual pronunciation by a certain
amount of time.

But then, pray tell, how many centuries does
the spelling of English lag behind?

:)

Haukur