I'm just starting to get caught up from having been more
than a bit under the weather for the last week. My sinuses
are still trying to drown Cleveland, but at least I'm no
longer running a significant fever.

> Þenna greip veit eg svo að Haraldi konungi fóstra mínum
> leikur mestur hugur á.

> Grabbed that (Am I correct that "Þenna" is the object, not
> the subject?),

Yes: it can only be masc. accus. sing.

> I know so that King Harald, my foster relative, most
> wishes for. (Z. hugr 3 - mér leikr h. á e-u, I long (wish)
> for a thing)

> I know this?? so that to King Harald, my foster-son, (his)
> mind is most bent upon.

> I know also that for King Haraldr my foster-son this
> treasure (acc of gripr, masc noun. I can only think that
> greip is a typo for grip as the noun greip (grip, clutch)
> is feminine) plays most on (his) mind (ie he longs for
> it).

My other edition does indeed have <grip> here.

> Sem þau komu til hellisdyra þau laukst upp hellirinn.

> When they came to (the) cave door they ooened up the cave
> (door).

> As they came to (the) cave door they opened up the cave.

> When they (ie Búi and Fríðr) came to (the) cave’s-doorway,
> then (I can only think that this is a typo for þá?)
> the-cave (masc nom sg with suffixed def art) opened up.

My other edition does indeed have <þá> instead of the second
<þau>.

> Hvergi mun eg leiða þig.
> I will not guide you at all.
> I will lead you nowhere?
> I will lead (guide, look after?) you not-at-all.

I think that she's telling him that she'll offer no guidance
in how to treat the boy (if it is a boy), but that he'd
better get it right, because if he doesn't, he'll not be
happy with the consequences.

> Gekk Búi leið sína og létti eigi fyrr en hann kom til
> Rauðs.

> Bui went on his way and didn't stop until he came to Red's
> (place).

> Bui went on his way and did not stop before he came to
> Raud.

> Búi went on his way and stopped not before he came to
> Rauðr.

Rob: <Til> takes the genitive, so it really is just 'to
Rauð'.

> ... því trölli er eg veit mest í Noregi.
> ... that troll who I know most in Norway.
> ... the troll which I know most in Norway.
> ... that troll ... which I know (to be) (the) greatest
> (largest?) in Norway.

I think that I'd go with 'greatest', in a general sense
encompassing trollishness and probably size as well.

Brian