Heil Alfta!

Keep up the good work.

> Þorbjörn hét maðr; hann var kallaðr Götuskeggr.
> Thorborn was called, a man; he was called Gate-beard.

Correct.

> Hann bjó í Austrey í Færeyjum. Guðrún hét kona hans.
> He lived in Austrey in the Faroes. Gudrun was called, wife his.

Correct.

> Þau áttu tvá sonu; hét Þorlákr inn ellri, en Þrándr inn yngri.
> They had two sons; called Thorlakr the elder and Thrandr the younger.

Correct.

> Þeir váru efniligir menn. Þorlákr var bæði mikill ok sterkr;
> They were promising men. Thorlakr was both tall and strong;

Correct.

> Þrándr var ok með því móti þá er hann þroskaðisk,
> Thrandr was also in that degree, as him, grown up,

Close.

> ******This was a difficult part. I noticed that in the vocabulary “með
> því móti” was given as “in that way.” Would “in that degree” be a
> possible translation here at all? Was I close at all in translating “er”
> as “as”?

Not quite. The 'með því móti' is probably best translated
as Konrad suggested. The 'er' is 'when' in this case.

Þrándr var ok með því móti þá er hann þroskaðisk.
Thrond was also with that form then when he developed.

> en miseldri þeira broeðra var mikit.
> but the disparity between the brothers was great.

Correct. "Disparity of age", that is. "Mis-age."

> Þrándr var rauðr á hár ok freknóttr í andliti, fríðr sýnum.
> Thrandr was red of hair and freckled of face, handsome showing
> (looking?).

Correct.

> Is Fríðr sýnum usually just translated as “handsome”? Is
> handsome-looking a possibility here at all?

Of course.

> Þorbjörn var auðigr maðr ok var þá gamall, er þetta var tíðenda.
> Thorbjorn was a rich man and was then old, when these were tidings.

Correct.

> Þorlákr kvændisk þar í eyjunum ok var þó heima með föður sínum í Götu.
> Thorlakr was married there on the island and was yet home with father
> his in Gate.

Almost correct. Note that 'eyjunum' is plural.
(Bonus question: What would the singular look like?)

> Ok bráðliga er Þorlákr var kvæntr andaðisk Þorbjörn Götuskeggr,
> But soon after Thorlakr was married, breathed his last Thorbjorn
> Gate-Beard,

Correct.

> ok var hann heygðr ok út borinn at fornum sið,
> and was he buried in a mound and out carried in the old way,

Correct.

> því at þá váru heiðnar allar Færeyjar.
> because then were heathens all of the Faerings.

See my comments on the previous answers.
It's not the inhabitants but the land itself
that the adjective refers to. Look at the endings:
heiðn-AR all-AR Færeyj-AR

> Synir hans skiptu arfi með sér, ok vildi hvártveggi hafa heimabólit í
> Götu,
> (To) sons his divided the inheritance for each, and willed each of the
> two to have the homestead in Gate,

Uhh... not quite. Word for word.

Synir hans skiptu arfi með sér
Sons his divided inheritance with themselves

ok vildi hvártveggi hafa heimabólit í Götu
and would each have the homestead in Gata

> því at þat var in mesta gørsimi. Þeir lögðu hluti á, ok hlaut Þrándr.
> because that was of the greatest value. They cast lots about it, and it
> was acquired by Thrandr.

Correct.

> ******These last two gave me the most trouble. Especially lögðu, can
> you talk about this one a bit? I never did figure out lögðu out and
> ended up referring to the translation at the Northvegr site, on it. Is
> this a form of leggja?

Yes. It is the preterite (past-tense). The preterite of a
weak verb like 'leggja' is formed with a dental suffix.

Present:

ek legg
þú leggr
hann leggr
vér leggjum
þér leggið
þeir leggja

Preterite:

ek lagða
þú lagðir
hann lagði
vér lögðum
þér lögðuð
þeir lögðu

In any language learning the various forms of verbs takes
a lot of effort. When I was a child I was made to memorize
English verbs like:

bring - brought - brought
sing - sang - sung
teach - taught - taught

No easy way to do it - just a lot of reciting over and over :)

In Old Norse you have to learn four forms of each verb; you can
figure the rest out from those. In this case:

leggja - lagða - lögðum - lagt

Since 'leggja' is a weak verb you theoretically don't need
the third form.

> From the vocabulary and since the other words I
> could figure out, I think it must be, yes? Also I was not
> really sure about how exactly to translate “á” in this sentence.

It's a difficult sentence.

> I was kind of
> disappointed with how I did on this last sentence because the rest I was
> able to get somewhat, after enough work but this last sentence gave me a
> really rough time.

I think you did rather well :-) To get even more out of this
you would probably benefit from reading some grammar. If you
haven't already got Barnes' grammar I suggest you buy it. It's
clear, correct and tells you exactly what you need to know. Gordon
is much more difficult if you don't already know Latin, some Greek,
and either French or German.

Kveðja,
Haukur