Here´s my translation

Alan

En er sumar kom þá gengu skip landa í milli. Þá spurðust þau tíðindi til
But when summer came, then ships (plural because gengu is 3rd pers plural past tense of ganga) went between (the) lands (ie from country to country). Then those tidings were-reported to

Noregs af Íslandi að það var alkristið. Varð Ólafur konungur við það allglaður
Norway from (ie out of) Iceland that it (ie Iceland) was entirely-Christian (note: alkristinn, not alkristnaðr). King Ólafr became very joyful with that (news)

og gaf leyfi öllum til Íslands þeim mönnum er hann hafði í gíslingum haft
and gave leave (to go) to Iceland to all those persons (men) whom he had had (kept) under guard (ie in our keeping, as hostages)

og fara hvert er þeim líkaði.
and to travel (infinitive) whithersoever (it) pleased them.

Kjartan svarar því að hann var fyrir þeim mönnum öllum er í gíslingu höfðu verið haldnir:
Kjartan answers because he was before (ie foremost of, see fyrir, Z8) all those persons (men)who had been held under guard (in our keeping, as hostages):

"Hafið mikla þökk og þann munum vér af taka að vitja Íslands í sumar."
“Have (receive, accept, 2^nd pers plural  imperative) (our) great thanks and we will (simple future tense) choose (see taka e-t af, Z12) that, to visit Iceland this summer.”

Þá segir Ólafur konungur: "Eigi munum vér þessi orð aftur taka Kjartan en þó
Then King Ólafr says: “We will not take back (ie recant) these words, Kjartan , but nevertheless

mæltum vér þetta ekki síður til annarra manna en til þín því að vér virðum svo
we spoke (ie addressed) this not less (ie more) to (the) other persons (men) than to you because we so consider,

Kjartan að þú hafir hér setið meir í vingan en gíslingu. Vildi eg að þú
Kjartan, that you have settled here more in friendship than in (our) keeping (ie as a hostage, gisling is an o-stem feminine noun, see Gordon 83, and many of these have a -u ending in the dative singular. This is typical of feminine nouns ending in –ing or –ung. Ingibjörg also follows this paradigm). I would-want (subjunctive) that you

fýstist eigi út til Íslands þó að þú eigir þar göfga frændur
desired not (to go) out to Iceland even though you have there noble kinsmen

því að kost muntu eiga að taka þann ráðakost í Noregi er engi mun slíkur á Íslandi."
because you-will have (the) opportunity to take that state-of-life (situation) in Norway which no-one similar will (have) in Iceland.”

Þá svarar Kjartan: "Vor herra launi yður þann sóma er þér hafið til mín gert
Then Kjartan answers: “Our Lord reward you (for) that honour which you have given to me

síðan er eg kom á yðvart vald. En þess vænti eg að þér munuð eigi síður gefa
since (see síðan er, Z5) I came under your power. But this I hope for, that you will not less give

mér orlof en þeim öðrum er þér hafið hér haldið um hríð."
to me permission than to those others whom you have here held for-a-while.”

Konungur kvað svo vera skyldu en segir sér torfengan slíkan mann ótiginn sem Kjartan var.
(The) king declared (it) should be so but says for himself such untitled a man (a commoner) as Kjartan was (to be) hard-to-get-hold-of. (ie it is not easy for him to find such a man)


Þann vetur hafði Kálfur Ásgeirsson verið í Noregi og hafði áður um haustið
That winter Káfr Ásgeirr’s-son had been (stayed) in Norway and had before during the-autumn

komið vestan af Englandi með skip þeirra Kjartans og kaupeyri. Og er Kjartan
come from-(the)-west from England with their, Kjartan (and his, remember Kjartan and Kálfr went halves in the ship) ship and cargo. And when Kjartan

hafði fengið orlofið til Íslandsferðar halda þeir Kálfur á búnaði sínum.
had received permission for an Iceland-journey, they, Kálfr (and he) hold to (ie go on with, see halda á, Z.iii) their preparations (for the journey).

Og er skipið var albúið þá gengur Kjartan á fund Ingibjargar konungssystur.
And when the ship was fully-equpped then Kjartan goes (on foot) to a meeting with (ie to see) Ingibjörg, (the) king´s-sister.

Hún fagnaði honum vel og gefur rúm að sitja hjá sér og taka þau tal saman.
She greeted him well and gives (makes) room (for him) to sit beside her and they take conversation together.

Segir Kjartan þá Ingibjörgu að hann hefir búið ferð sína til Íslands.
Kjartan says then to Ingibjörg that he has made-ready for his journey to Iceland.

Þá svarar hún: "Meir ætlum vér Kjartan að þú hafir gert þetta við einræði þitt
Then she answers: “We think (3^rd pers pl present), Kjartan, that you have done this more with your self-will (simply the noun, einræði) (ie from your own motives)

en menn hafi þig þessa eggjað að fara í brott af Noregi og til Íslands."
than (that) men have egged you on to this, to go away from Norway and to Iceland.”