Here’s my translation

Alan

Skúli hét sá maðr er þá tók forráð yfir liðinu. 
That man was-called Skúli, who then took charge over the-troops.

Sigldu þeir síðan heim í Garðaríki, ok sögðu konungi slík tíðindi sem orðit höfðu í þeira ferðum. 
They sailed after-that home to Garðaríki, and said to (the) king such tidings as had happened in their travels (plural).

Konungr lét sér fátt um finnast en Sigrgarðr var mörgum manni harmdauði.
(The) king paid little heed to (it) (finnast, Z9, ie didn´t appear to be overly concerned by the news) but Sigraðr was to many a person (man) a sorrowful-death (ie Sigrgarðr’s death was a great sorrow).

Fréttust þessi tíðindi nú víða. 
These tidings were now reported widely.

Þessi tíðindi komu austr í Tartaría til eyrnanna meykonunginum en hon brosti við ok kvað margt skrökvat þó at skemmra væri at spyrja en þó sáu menn þá at hagl hraut ór augum henni rautt sem blóð.
These tidings came east to Tartaría to the-ears (eyra, gen pl + def art) of the-maiden-king but (and) she smiled-in-response and declared many (a tale) invented even-though (one) was to be-informed of (them) (spyrja, Z4) in a shorter-time (comparative, skemmr) (ie even in cases of more recent events or more immediate/direct reporting) but nevertheless people (men) saw then that hail flew out of her eyes, red like blood.

Annat sumar eptir at áliðnu sumri sigldi Knútr inn knappi austr í Tartaría. 
(The) following summer after at (the) passing of summer, Knútr the brisk (knob) sailed east to Tartaría.

Hann rataði strauma stóra ok storma mikla, ok leysti skipin undir þeim. 
He met-with (rata, Z2) strong currents (lit: large streams) and great storms, and the ships broke-up under them (leysta, Z2, impers).

Komst Knútr einskipa undir Tartaría, ok braut skipit í lending ok misti menn alla nema tólf eina. 
Knútr made-his-way with-a-single-ship under Tartaría and the-ship broke (apart) at (the) landing-place and (they) lost people (men) all except twelve only.

Fjárhlut rak á land allan. 
(The) entire (masc acc sg) property (masc acc sg) was-tossed (reka, Z7, impers) on to land (shore)

Spurðu menn hann hvað ráðs skyldi taka. 
People (men) asked him what (sort) of plan (they) should adopt (take)

Knútr sagði ekki annat til enn at reyna á drengskap meykonungsins. 
Knútr told (them) nothing other than to make a trial on (the) high-mindedness (seems to fit the context better than ‘courage’ here) of the-maiden-king.

Hörðr segir at væri gæfuraun, en Stígandi segir at ekki dygði ófreistað, at einum degi gengu þeir fyrir meykonunginn.
Hörðr says that (it) was a trial-of-luck, but Stígandi says that nothing sufficed (duga) untested (ú + pp of freista) (doing nothing proved nothing, “nothing ventured nothing gained”), (so) that on one day they went before the-maiden-king.

Sat hon þá yfir borðum. 
She sat then at table.

Knútr kvaddi hana virðuliga sem henni sæmdi. 
Knútr greeted her respectfully as (one) should-honour her.

Hon tók ei kveðju hans en spurði þó hvat manni hann væri. 
She accepted not his greeting but asked nevertheless what (sort of) person (man, dat sg) he was.

Hann kvaðst Knútr heita, “ok er ek kominn hér á yðrar náðir. 
He declared-of-himself to be-called Knútr, “and I am (have) come here for your protection.

Hefir oss tekist heldr slysliga, misst skip vár öll, en tókum land með skipbroti, ok vildum vér gjarnan þiggja hér vetrvist. 
(it) has happened to us rather unfortunately, lost all our ships, but (and) (we) reached land with a shipwreck, and we wanted eagerly (lit: willingly, gjarnan, CV) to receive here winter-abode.

Skortir oss ei fé fyrir oss at leggja, eðr aðra þjónustu ef þér vilit.”
(It) lacks not for us (ie we are not lacking) money to pay for ourselves, or other service if you want.”

Hon horfði á hann lengi ok þagði, en litlu síðar mælti hon: “ertu sá Knútr er drepit hefr Sigrgarð inn frækna?”
She was turned to (ie faced) him for a long time and was-silent, but a little later she spoke: “Are-you that Knútr who has killed Sigrgarðr the brave?”

“Ei mun ek þess þræta sem aðrir menn kenna mér; vænti ek þar helst fyrir sæmda af yðr er ek réði af yðr þann ófrið.”
“I will not deny that which other people (men) attribute to me (charge me with, kenna, Z3, Z4); I hoped (vænta) most-rather for honour there-for (for that), when I did-away-with (ráða af, Z16) that hostility (úfríðr, noun) to you.”