Here’s my translation

Alan

Kjartan tók vel undir þetta og kvað hana vel mála leita.
Kjartan readily took this on-board (lit: under) and declared her (to have done) well to seek speech(es) (to broach the subject, see mál, Z4, it is she who is doing the broaching) (I´m not sure if this is meant to be gen pl or is a typo for máls).

Eftir þetta er  komið saman tali þeirra Hrefnu. Tala þau um daginn. Um kveldið
After this their conversation, Hrefna´s (and Kjartan´s) is brought about (lit: come together, koma saman, Z4). They talk (present tense) during the-day. During the-evening

spurði Þuríður Kjartan hversu honum hefði virst (virðast) orðtak Hrefnu. Hann lét vel yfir,
Þuríðr asked Kjartan how (the) words (orðtak, Z3) of Hrefna had seemed (pp of virðast, Z3) to him. He expressed approval (láta vel yfir e-u, , Z12),

kvaðst kona þykja vera hin skörulegsta að öllu því er hann mátti sjá af.
declared-for-himself (the) woman to seem to be the finest in all that which he might contemplate (lit: see of, ‘look for’ seems to fit here. I don´t think ‘do without’ (sjá af, Z6) really fits the context here).

Um morguninn eftir voru menn sendir til Ásgeirs og boðið (bjóða) honum í Ásbjarnarnes.
During the morning after persons (men) were sent to Ásgeirr and (it was) offered to him (to come) (ie he was invited, but seems an odd way to express this) to Ásbjarnarnes.

Tókst nú umræða um mál þeirra og biður Kjartan nú Hrefnu dóttur Ásgeirs.
Discussion now began concerning their “affair” (situation) and Kjartan now asks now for Hrefna, Ásgeirr’s daughter (in marriage).

Hann tekur því máli líklega því að hann var vitur maður og kunni að sjá
He receives that speech favourably because he was a wise person (man) and would-be-able (present subjunctive) to see

hversu sæmilega þeim er boðið. Kálfur er þessa máls mjög flýtandi:
how honourably for them (it) is asked (ie the honour bestowed on them by the asking). Kálfr is much a-hastening of this matter (keen to get things rolling?):

"Vil eg ekki láta til spara."

“I want to let spare (hold back) nothing towards (it).”


Hrefna veitti og eigi afsvör fyrir sína hönd og bað hún föður sinn ráða.
Hrefna (incidentally J) gave also not a refusal for her part (lit: hand) and she asked her father to decide (ráða, Z6, I suspect is what she is asking, not merely to advise).  

Er nú þessu máli á leið snúið og vottum bundið. Ekki lætur Kjartan sér annað líka
(It) is now in this matter turned on course (ie concluded favourably) and bound with witnesses (contracted in the presence of witnesses). Kjartan declares (láta, Z10) no other (ie nothing else) to please him

en brullaup sé í Hjarðarholti. Þeir Ásgeir og Kálfur mæla ekki þessu í mót.
than (that the) wedding-feast be in Hjarðarholt. They, Ásgeirr and Kálfr spoke not against this.

Er nú ákveðin brullaupsstefna í Hjarðarholti þá er fimm vikur eru af sumri.
(The) wedding-meeting is now appointed in Hjarðarholt when five weeks are of summer (ie after the fifth week of summer).


Eftir það reið Kjartan heim með stórar gjafir. Ólafur lét vel yfir þessum tíðindum
After that Kjartan rode home with great gifts. Ólafr expressed approval of these tidings

því að Kjartan var miklu kátari en áður hann fór heiman.
because Kjartan was much more-cheerful than before he went from-home.

Kjartan fastaði þurrt langaföstu og gerði það að engis manns dæmum hér á landi
Kjartan dry-fasted (on fish-and-veg (probably lentils J) at Lent (lit: long-fast) and did that out of (based on, at, Z.iv.8) the precedents of no man here in (the) country

því að það er sögn manna að hann hafi fyrstur manna fastað þurrt hér innanlands.
because that is (the) report of persons (ie the story goes) that he would-have fasted on fish first of people (men) here within-the-land (ie he would have been the first person to dry-fast in Iceland).

Svo þótti mönnum það undarlegur hlutur að Kjartan lifði svo
That seemed to people (men) such a wondrous thing that Kjartan lived so

lengi matlaus að menn fóru langar leiðir að sjá hann.
long without-meat (meatless, mat, Z2 + lauss) that men travelled long roads (great distances) to see (look at) him.

Með slíku móti voru aðrir hættir Kjartans umfram aðra menn. Síðan gengu af páskarnir.
In like manner were Kjartan’s other ways-of-doing-things beyond (the ken? ability? of) other men. After-that, the-Passion (Easter) passed (lit: went off)

Eftir það láta þeir Kjartan og Ólafur stofna til veislu mikillar.
After that they, Kjartan and Ólafr caused to arrange a great banquet.

Koma þeir norðan, Ásgeir og Kálfur, að á kveðinni stefnu og Guðmundur og Hallur og
They come (present tense) from-the-north, Ásgeirr and Kálfr, at (the) appointed time (stefna, Z3) and Guðmundr and Hallr and

höfðu þeir allir saman sex tigu manna. Þeir Kjartan höfðu og mikið fjölmenni
they had all together six-tens of (ie sixty) men. They, Kjartan (and Ólafr) had also a great crowd-of-people

fyrir. Var sú veisla ágæt því að viku var að boðinu setið.
before (ie already there). That feast was excellent because (there) was a week sat (pp of sitja)  at the-wedding-feast (boð) (ie the feast lasted a week).

Kjartan gaf Hrefnu að línfé moturinn og var sú gjöf allfræg því að engi var þar svo
Kjartan gave to Hrefna as (at, Z.iv.2) (the) bridal-gift the-head-dress and that gift was very-famous because no-one was there so

vitur eða stórauðigur að slíka gersemi hefði séð eða átta.
wise or very-wealthy that (they) had seen or owned such a treasure (acc fem sg).