Here’s my translation

Alan

Kjartan gerir svo sem faðir hans beiðist og tekur hann nú upp skarlatsklæði sín
Kjartan does just as his father asked-for-himself and he now chooses (lit: takes up) his clothes-of-scarlet

þau er Ólafur konungur gaf honum að skilnaði og bjó sig við skart.
those which King Ólafr gave him at (their) parting and arrayed (dressed, búa, Z2) himself with (in) finery (cf  búa sik í skart).

Hann gyrti sig með sverðinu konungsnaut. Hann hafði á höfði hjálm gullroðinn og
He girded himself with the-sword (that was the) king’s-gift. He had (wore) on (his) head a gilt (lit: gold-reddened) helmet and-

skjöld á hlið rauðan og dreginn á með gulli krossinn helgi.
a shield at (his) side, red and with the gold cross of holiness (security?) drawn on (it).

Hann hafði í hendi spjót og gullrekinn falurinn á. Allir menn hans voru í litklæðum.
He had in hand a spear and the gold-inlaid spear-head-socket on (it). All his men (people) were in coloured (dyed)-clothes.

Þeir voru alls á þriðja tigi manna. Þeir ríða nú heiman úr Hjarðarholti og fóru
They were in the third ten of men (ie there were somewhere between 20 and 30 of them) all up. They ride now from home out-of Hjarðarholt and went

þar til er þeir komu til Lauga. Var þar mikið fjölmenni fyrir.
until they came to Laugar. A great crowd-of-people were there before (ie already)

45. kafli - Af Kjartani og Bolla
Chapter 45 – Of Kjartan and Bolli

Bolli gekk í móti þeim Ólafi og synir Ósvífurs og fagna þeim vel. Bolli gekk
Bolli walked towards (ie to meet) them, Ólafr (and co) and Ósvífr’s sons (nominative) also greeted them well. Bolli walked

að Kjartani og minntist til hans. Kjartan tók kveðju hans.
towards Kjartan and kissed him. Kjartan received his greeting (but not so well, it would seem).

Eftir það var þeim inn fylgt. Bolli er við þá hinn kátasti. Ólafur tók því einkar vel en
After that (it) was guided for them inside (ie they were lead inside). Bolli is towards (við, Z.ii.6) them (pronoun) the most-cheerful (you´re overdoing it, lad!). Ólafr took that exceedingly well but

Kjartan heldur fálega. Veisla fór vel fram.
Kjartan rather coldly. (The) feast (no wedding) proceeded (li: went forward) well.

Bolli átti stóðhross þau er best voru kölluð. Hesturinn var mikill og vænn
Bolli had those stud-horses which were called best. The stallion (is specifically identified here, the others horses in the group were mares) was tall and beautiful (so far as horses go, if your into horses, and Kjartan isn´t)

og hafði aldregi brugðist að vígi. Hann var hvítur að lit og rauð eyrun og toppurinn.
and had never failed in battle. He was white of colour and the ears red and the-forelock.

Þar fylgdu þrjú merhryssi með sama lit sem hesturinn.
There three mares accompanied (him) with the same colour as the-stallion.

Þessi hross vildi Bolli gefa Kjartani en Kjartan kvaðst engi vera hrossamaður og vildi eigi þiggja.
Bolli wanted to give these horses to Kjartan but Kjartan declared-of-himself not to be a horseman (does he mean horseman, generally, or more pointedly groom?, see hrossmaðr, Z1) and wanted not to accept (them).

Ólafur bað hann við taka hrossunum "og eru þetta hinar virðulegstu gjafir."
Ólafr bade him to accept the-horses (as far as I can tell, Z12 identifies only the dative, taka við e-u, taka vel við e-m) “and this (lot) (I hope that sort of explains it, I can´t give a grammatical explanation but there have been several instances of sg pronoun referring to a plural  in the text so far, þetta is neut nominative (subject) sg) are the most-worthy gifts.”


Kjartan setti þvert nei fyrir, skildust eftir það með engri blíðu og fóru Hjarðhyltingar
Kjartan flatly refused (lit: set no adversarily against (them)), (they) parted-company after-that with no friendliness and (the) Hjarðaholters went

heim og er nú kyrrt. Var Kjartan heldur fár um veturinn.
home and (it) is now quiet. Kjartan was rather down-in-the-dumps during the-winter.

Nutu menn lítt tals hans. Þótti Ólafi á því mikil mein.
People (men) little had-the-benefit of his conversation. (It) seemed to Ólafr a great pity (harm) in that.

Þann vetur eftir jól býst Kjartan heiman og þeir tólf saman. Ætluðu þeir
That winter, after Yule, Kjartan readies-himself (to go) from home and they twelve together. They intended (to go)

norður til héraða. Ríða nú leið sína þar til er þeir koma í Víðidal norður í Ásbjarnarnes
north to (the) country (typo: herað?). (They) ride now on their way (there´s no kjörr ok skóga on this road, look at  riða, Z1 again!) until the come into Víðidalr (Willow-Dale) north in Ásbjarnarnes

og er þar tekið við Kjartani með hinni mestu blíðu og ölúð.
and Kjartan (note: still dative in passive construction) is there received with the most friendliness and affection.

Voru þar híbýli hin veglegstu. Hallur son Guðmundar var þá á tvítugs aldri.
Was there the most-magnificent homestead (note: plural). Hallr son of Guðmundr was then in the age of twenty (ie twenty years old)

Hann var mjög í kyn þeirra Laxdæla. Það er alsagt að eigi hafi verið
He was much in (the) kinship(´s mould)(presumably he took after his kin) of those Laxdalers. That is spoken-of-by-all that (there) had not been

alvasklegri maður í öllum Norðlendingafjórðungi. Hallur tók við Kjartani
a more-valiant person (man) in all (the) Quarter-of-the-Northern-land-folk. Hall received Kjartan

frænda sínum með mikilli blíðu
his kinsman with great friendship.