Heil Arlie!

Your translation is good. Just a few points.

> hann byggði fyrstr manna Færeyjar
> (he dwelt first of the Færey men)

Not quite. Very literally this is:

hann byggði fyrstr manna Færeyjar
he settled first of men the Faroes

> sumir leituðu til annarra eyðilanda
> some sought for another uninhabited land

Plural there - 'other uninhabited lands'.

> ok gifti þar Ólöfu dóttur Þorsteins rauðs,
> and gave [in marriage] there to Ólöf daughter of Þorstein the red,
>
> [this has got to be wrong ... more likely would
> be that she gave her daughter Ólöf in marriage to
> Þorstein the red ... but that's not what the grammar
> seems to be telling me.]

Well... as it stands it is actually ambiguous;
from a purely grammatical standpoint it could
mean either:

1. She gave Ólöf to the daughter of Þorsteinn rauðr.

or

2. She gave Ólöf [who was] the daughter of Þorsteinn rauðr

What grammar can't tell you but your good sense will
is that the latter option is the correct one.

This Ólöf was actually Auðr's granddaughter - Þorsteinn
was Auðr's son, killed in battle some time before this.

Another source tells us:

"Auðr hélt fyrst til Færeyja, ok gaf þar Álöfu,
dóttur Þorsteins rauðs; þaðan eru Götuskeggjar komnir.
Síðan fór hon at leita Íslands."

> ok er þaðan kominn
> and from them (who/which/when from there) came

Literally this goes:

ok er þaðan kominn
and is thence come

> er þeir kalla Götuskeggja, er byggðu í Austrey.
> which they call (the) Götuskeggja, who dwelt in Austrey.

Well, 'Götuskeggjar' in nominative.

Kveðja,
Haukur