Here’s my translation

Alan

En fátt varð þeim að orðum þaðan í frá. Í þessu bili tekur Ingibjörg til
But little (I´m not sure about this but this seems more likely to me than “coolness” here, which given Z2’s examples would more likely be “fátt var með/í milli þeim”) befell them by-way-of words from that moment (ie they didn´t say much to each other after that). At this moment Ingibjörg has-recourse-to (ie turned her attention to, see taka til, Z12)

mjöðdrekku er stendur hjá henni. Hún tekur þar úr motur hvítan, gullofinn,
a mead-cask (mjöðdrekka) not mjöðdrykkja)  (for a moment there I too thought she had resorted to drink!) which stands beside her. She takes there-from a lady’s-headgear, white and gold-woven,

og gefur Kjartani og kvað Guðrúnu Ósvífursdóttur helsti gott að vefja honum
and gives (it) to Kjartan and declared (it) for Guðrún (fem dat sg. See Gordon 83 again as with Ingibjörg last time) Ósvífr’s-daughter more than good enough (I think this is helzti rather than helzt, which I think produces a slightly different intended meaning) to wrap

að höfði sér "og muntu henni gefa moturinn að bekkjargjöf. Vil eg að þær
around her head “and you-will give her the-head-gear as a “bench-gift” (from bridegroom to bride as wedding gift). I want that they,

Íslendinga konur sjái það að sú kona er eigi þrælaættar er þú hefir tal átt við í Noregi."
Icelandic women, should-see that this woman* (ie I, Ingibjörg) is not slave-descended (ie of no mean extraction) *with whom (refers back to sú kona) you had conversation (and probably much else besides) in Norway.“

Þar var guðvefjarpoki um utan. Var það hinn ágætasti gripur.
There was a bag-of-fine-woven-cloth around outside (it) (ie enclosing it). That was the most-excellent item-of-value.

"Hvergi mun eg leiða þig," sagði Ingibjörg, "far nú vel og heill."
“I will lead (conduct) you not at all (ie down to your ship),” said Ingibjörg, “fare now well and hail.”

Eftir það stendur Kjartan upp og hvarf til Ingibjargar og höfðu menn það
After that Kjartan stands up and turns-in-leave-taking to kiss (see hverfa til e-s, Z3 but M&M’s student text glosses: hverfa til = kyssa (to kiss), MM&HP render it: embrace, which I can´t really see) to Ingibjörg and men owned that

fyrir satt að þeim þætti fyrir að skiljast.
for true (ie they were convinced) that (it) was for them (K and I) hard (see e-m þykkja fyrir, Z2) to part-company.

Gengur nú Kjartan í brott og til konungs, sagði konungi að hann er þá búinn
Kjartan now walks away and to (the) king, said to (the) king that he is then ready

ferðar sinnar. Ólafur konungur leiddi Kjartan til skips og fjöldi manns með honum.
for his journey. King Ólafr leads (conducts) Kjartan to (the) ship and a multitude of men (persons, note: grammatically gen sg.) with him.

Og er þeir komu þar sem skipið flaut og var þá ein bryggja á land.
And when they came there where the-ship was-floating also (ok, Z6?) (there) was then a single gangway to land (shore).

Þá tók konungur til orða: "Hér er sverð Kjartan er þú skalt þiggja af mér að
Then (the) king took to words (started speaking): “Here is a sword, Kjartan, which you shall accept from me at

skilnaði okkrum. Láttu þér vopn þetta fylgjusamt vera því að eg vænti þess
our parting. Let(-you) this weapon be attached to yourself (ie keep it by you at all times) because I expect that,

að þú verðir eigi vopnbitinn maður ef þú berð þetta sverð."
that you should-become not a weapon-bitten man (person) (a casualty of battle with sharp or pointy sticks) if (ie so long as) you carry this sword.”

Það var hinn virðulegsti gripur og búið mjög.
That was the most-splendid treasure and much adorned.

Kjartan þakkaði konungi með fögrum orðum alla þá sæmd og virðing er hann
Kjartan thanked (the) king with fair words for all that honour and honour (for want of a better word J) which he

hafði honum veitt meðan hann hafði verið í Noregi.
had granted to (bestowed on) him while he had been in Norway.

Þá mælti konungur: "Þess vil eg biðja þig Kjartan að þú haldir vel trúna."
Then (the) king spoke: “I want to ask that of you Kjartan, that you hold (maintain) well the-faith .”

Eftir það skiljast þeir konungur og Kjartan með miklum kærleik. Gengur þá Kjartan út á skip.
After that they, king and Kjartan, part-company with great amity. Then Kjartan walks out onto (the) ship.

Konungurinn leit eftir honum og mælti: "Mikið er að Kjartani kveðið og kyni hans
The-king looked after him and spoke: “Much is (vera) inflicted (determined by fate) (past part of kveða e-t at e-m, Z3) on Kjartan and his kin (ie there´s will be a hard lot)

og mun óhægt vera atgerða við forlögum þeirra."
and (it) will be difficult of accomplishments (gen plural of atgörð I think; if it was a past participle = accomplished, I would have expected atgert) with their destiny.”