Here’s my translation

Alan

Ósvífurssynir fóru utan það sumar og kom engi þeirra út síðan.
(The) sons of Ósvífr went abroad that summer and not-one (masc sg rather than neut pl I think) of them came back-to-Iceland (lit: out, út) after-that.

Lauk þar eftirmáli að Ólafur þótti hafa vaxið af því að hann lét þar með beini ganga
(It) was-concluded there in (the) actions-against the slayers (ie the outcome of the case was) that Ólafr seemed to have grown (in standing) from that, that (ie because) he dealt harshly (lit: caused to go with/ through? (the) bone, see bein, Z1) there

er maklegast var, þar er þeir voru Ósvífurssynir, en hlífði Bolla fyrir
which was most-fitting, there where (ie when) they were Ósvífr’s-sons, but spared Bolli for

frændsemis sakir. Ólafur þakkaði mönnum vel liðveislu. Bolli hafði landkaup
reasons of kinship. Ólafr thanked well people for (their) support. Bolli had a land-deal (ie bought a property)

í Tungu að ráði Ólafs.
in Tunga (Tongue) on Ólafr’s advice.

Það er sagt að Ólafur lifði þrjá vetur síðan Kjartan var veginn. En síðan er
That is said that Ólafr lived three winters after Kjartan was slain. But after

hann var allur skiptu þeir synir hans arfi eftir hann. Tók Halldór bústað í
he was was dead (see allr, Z4) those sons divided his estate after him (what he left for their inheritance). Halldórr took (the) abode in

Hjarðarholti. Þorgerður móðir þeirra var með Halldóri. Hún var mjög
Hjarðarholt. Þorgerðr, their mother, was (stayed) with Halldór. She was very

heiftarfengin til Bolla og þótti sár fósturlaunin hans og ómaklega á koma.
seized-by-spite towards Bolli and the-‘rewards’-for-(the)-fostering (nom neut plural) of him seemed painful (sár, Z2) (to her) and to have-been-effected (see koma á, Z4) unjustly.

52. kafli
Chapter 52

Þau Bolli og Guðrún settu bú saman um vorið í Sælingsdalstungu og varð það brátt reisulegt.
They Bolli and Guðrún established (the) farm together during the-spring in Sælingsdalstunga and that soon became stately.

Þau Bolli og Guðrún gátu son. Þeim sveini var nafn gefið og
They Bolli and Guðrún begat a son. To that lad was given a name and

kallaður Þorleikur. Hann var vænn sveinn snemma og vel fljótlegur. Halldór
called Þorleikr. He was a promising lad early (ie from a young age) and amply speedy. Halldór

Ólafsson bjó í Hjarðarholti sem fyrr var ritað. Hann var mjög fyrir þeim bræðrum.
Ólafr’s-son lived in Hjarðarholt as was written before. He was greatly superior to those brothers (ie he was the foremost of the brothers, see fyrir, Z8)


Það vor að Kjartan var veginn tók Þorgerður Egilsdóttir vist frændsveini sínum
That Spring that Kjartan was slain, Þorgerðr Egill’s-daughter took (obtained) a stay (ie arranged lodgings) for her young kinsman

með Þorkatli að Hafratindum. Sveinninn gætti þar fjár um sumarið.
with Þorkell at Hafratindar (He-goat-Peaks). The lad took-care-of (tended) there sheep during the-summer.

Honum var Kjartan mjög harmdauði sem öðrum. Hann mátti aldrei tala til
By him was Kjartan much lamented (harmdauðr, adj)as by others. He could never speak of (see tala vel/illa til e-s, under til, Z1

Kjartans svo að Þorkell væri hjá því að hann mælti jafnan illa til hans og
Kjartan such that (in situations where) Þorkell was nearby because he (ie Þorkell) spoke always badly of him and

kvað hann verið hafa hvítan mann og huglausan og hermdi hann oft eftir
declared him to have been a white (we would say yellow) person and cowardly and he repeated (re-enacted) often after (ie in imitation of) (him)

hvernig hann hafði við orðið áverkann. Sveininum varð að þessu illa getið og
how he (ie Kjartan) had become with (ie reacted, responded to, see verða við, Z8) the-bodily-injury. To the-lad (it) became ill-gotten from this (ie he became unsettled by this, geta, Z1) and

fer í Hjarðarholt og segir til Halldóri og Þorgerði og bað þau viðtöku.
(he) goes (present tense) to Hjarðarholt and says to Halldór and Þorgerðr and begged them for reception (ie to take him in).

Þorgerður bað hann vera í vist sinni til vetrar.
Þorgerðr bade him to be (stay) in his (present) lodgings until winter.

Sveinninn kvaðst eigi hafa þrótt til að vera þar lengur "og mundir þú mig eigi biðja þessa
The-lad declared-of-himself not to have strength to stay there longer “and you would not ask me this

ef þú vissir hversu mikla raun eg hefi af þessu."
if you knew how much grief I have from this.”

Þá gekkst Þorgerði hugur við harmtölur hans
Then (the) feeling in Þorgerðr is-altered towards his lamentations  (ie she is moved to compassion by his lamentations, see gangast, Z15)

og kvaðst mundu láta honum uppi vist fyrir sína hönd.
and declared-of-herself (that she) would grant lodgings for him for her part.

Halldór segir: "Gef ekki gaum sveini þessum því að hann er ómerkur."
Halldór says: “Give not attention  to (take no notice of) this lad because he is insignificant (a nobody).”