Hi Simon!

> In modern Icelandic, the U in SUMAR is long
> as it is followed by only one consonant.

True.

> What happens, e.g. in SUMRIN - does the vowel
> stay long, or get shortened?

It gets shortened.

> What happened in analogous cases in Old Norse?

Nothing. In Old Norse /u/ is always [u] regardless
of position and /ú/ is always [u:] regardless of
position. At least in theory.

Kveðja,
Haukur