Hello :-)

You're doing very well, Arlie.

> I guessed borinn for a past participle of bera.
> That didn't entirely make sense.

It is true, nevertheless.

> Þorbjörn hét maðr; hann var kallaðr Götuskeggr.
> A man was named Þorbjörn: he was called Götuskeggr. (Gata(???)'s Beard?)

Good.

> Hann bjó í Austrey í Færeyjum. Guðrún hét kona hans.
> He lived in Austrey in the Faroes. His wife was named Guðrún.

Good.

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

Exactly.

> Þeir váru efniligir menn.
> They were promising men.

Correct.

> Þorlákr var bæði mikill ok sterkr;
> Þorlákr was both big and strong;

Correct.

> Þrándr var ok með því móti þá er hann þroskaðisk, en miseldri þeira
> broeðra var mikit. Þrándr was the same (lit. "also along with that
> manner") when he had grown to full strength (þroskaðisk could be simply
> "was fully grown", but strength seems implied), and the disparity of
> age between the brothers was large.

That was a very difficult sentence but you got it exactly right.
One very minor point: In this case I would translate 'en', as
'but' rather than 'and'.

> Þrándr var rauðr á hár ok freknóttr í andliti, fríðr sýnum.
> Þrándr was a handsome looking redhead with a freckled face
> (more lit.: Þrándr was red of hair and freckled in face, handsome to
> sight.)

Very good.

> Þorbjörn var auðigr maðr ok var þá gamall, er þetta var tíðenda.
> Þorbjörn was a rich man and was then old, when that (there? ??þetta??)
> was news.

More or less.

Literally: Þorbjörn was a wealthy man and was then old when this
was [of] tidings.

As sensum: Þorbjörn was a wealthy man and he was old when the events
described here took place.

> Þorlákr kvændisk þar í eyjunum ok var þó heima með föður sínum í Götu.
> Þorlákr married there in the islands and was nevertheless at home with
> his father at (in) Gata (???).

Correct.

> Ok bráðliga er Þorlákr var kvæntr andaðisk Þorbjörn Götuskeggr,
> But soon after (then) Þorlákr was married Þorbjörn Götuskeggr died,

Correct. You probably mean "(when)" where you wrote "(then)".

> ok var hann heygðr ok út borinn at fornum sið,
> and he was buried and carried out according to ancient customs

More or less.

Note that 'heygðr' is derived from 'haugr' = "mound".
Also note that 'fornum sið' is dative singular; thus I would
translate "according to the old custom". The old custom is,
in this case "heathenry".

> því at þá váru heiðnar allar Færeyjar.
> because at that time all in the Faroes were heathen.

Not quite. Or, at least, not literally.

"because at that time all the Faroes were heathen"

The land itself, rather than its inhabitants, is often
referred to as being heathen or christian. Other examples
from the literature:

"Land var alheiðit." = "The land was completely heathen."

"... hinn er fimm
á fám vetrum
lofða vinr
lönd kristnaði."

"... that friend of the people who christianized
five lands in a few winters."

[Yeah, that was king Olaf.]

For a counter-example king Harald Bluetooth bragged of
having converted the Danes - rather than Denmark itself.

The runes transcribed:

haraltr kunukR baþ kaurua kubl þausi aft kurm faþur sin
auk aft þaurui muþur sina sa haraltr ias saR uan tanmaurk
ala auk nuruiak auk t[a]ni [karþi] kristna

Latinized and normalized:

HaraldR konungR bað gørva kumbl þessi eft Gorm föður sinn
auk eft Þórvé móður sína - sá HaraltR es séR vann Danmörk
alla auk Norveg auk Dani gørði kristna.

13th century Icelandic:

Haraldr konungr bað gøra kumbl þessi eftir Gorm föður sinn
ok eftir Þórvé móður sína - sá Haraltr er sér vann Danmörk
alla ok Noreg ok Dani gørði kristna.

An additional translation assignment for you :-)

> Synir hans skiptu arfi með sér,
> his sons divided (the) inheritance among themselves,

Correct.

> ok vildi hvártveggi hafa heimabólit í Götu,
> and each one wanted to have the homestead in Gata (???),

Correct. But why do you throw in three question marks every
time you say 'Gata'?

> því at þat var in mesta gørsimi.
> because it was the most valuable.

Yes. More literally:
"because it was the greatest treasure".

> Þeir lögðu hluti á, ok hlaut Þrándr.
> They divided (the inheritance) into shares
> [prepared to a portion?] and Þrándr won it by lot.

Good attempt. But I think the meaning is:
"They cast lots for it - and Þrándr received [it]."

All-in-all this was a very good translation.

Kveðja,
Haukur