Here’s my translation

Alan

Hann færði sér þat vel í nyt því hann var svá tilhallr við konurnar, at hann missti aldrei einhverja, ok þótti þat mörgum mikit at um hans ráð at hann fekk aldrei svá væna konu eðr velættaða at hann sinnti lengr enn þrjár nætr, ok þótti ríkum mönnum mikil smán í at þeira frændkonur eðr dætr váru svívirðar. 
He well availed himself of that (foera sér e-t í nyt, under nyt), because he was so favourable to the-women, that he never was-without some (woman), and that seemed big (ie a big deal, a matter of great concern) to many (people) regarding his situation (ráð, Z7, or future marriage, match, Z8?), that he never got so beautiful a woman or well-descended (well-born) that he attended (on her)(ie paid attentions to her) still longer than three nights, and (there) seemed to powerful people (men) a great disgrace in (it) that their kinswomen or daughters were dishonoured.

En þeir urðu sjálfir svábúit at hafa, en engi þorði um at vanda. 
But (And) they needed to (verða at + inf) behave themselves just-the-same (svá búinn, ie toe the line, not stick their necks out) (?), but (and) no-one dared to complain about (it) (vanda, Z3)

Menn Sigrgarðs vöndu sik mjök eptir honum um kvennafarit. 
Sigrgarðr’s people (men) modelled (venja, Z1, Z2) themselves greatly after him concerning the-(his) going-after-women (‘womanising’)

Urðu þeir af því ei vinsælir en af þessu urðu þeir víðfrægir. 
They became (ie were) not popular for that (reason) but they became (ie were) renowned for this.

Sigrgarðr fór í hernað stundum ok veitti honum þat vel því at hann hafði sigr hvar sem hann barðist. 
Sigrgarðr went a-harrying sometimes and that turned-out well (proved fortunate) (veita, Z8) for him because he had victory wherever he did-battle.

Stundum fór hann fyrir land fram at skemta sér; sömu hélt hann fram um kvennafarit i hverju landi sem hann var.
Sometimes he journeyed all-along (the) land forward (?) to enjoy himself; he upheld (kept up, halda e-u fram, Z.iii) the same (practice (?)) concerning the-(his) going-after-women (‘womanising’) in each land (country) where he was.

þenna tíma réð fyrir austr i Tartaría konungr sá er Hergeirr hét. 
At this time, that King who was called Hergeirr (War Spear) maintained-authority (ie ruled) east in Tartaría.

Hann var gamall. 
He was old.

Hann átti þrjár dætr: ein hét Hildr, önnur Signý; Ingigerðr hét hin elsta. 
He had three daughters, one was-called Hildr, another Signý; the eldest was-called Ingigerðr.

Hon var allra meyja fríðust. 
She was of all maidens (girls) most-beautiful.

Hergeirr hafði snemma misst drottningar sinnar. 
Hergeirr had early on suffered-the-loss-of his queen

Váru dætr hans þá ungar en síðan tók hann at sér þá konu er Hlégerðr hét. 
His daughters were then (ie at the time of the queen´s death) young (fem plural, not comparative) and after-that he took to himself (as a wife) that (þá) woman who was-called Hlégerðr

Ókunnig var mönnum ætt hennar. 
Her ancestry was unknown (úkunnigr) to folk (men)

Hon átti tvá bræðr. 
She had two brothers.

Þeir váru miklir fyrir sér. 
They were strong (powerfulf) (see fyrir, Z.i.13)

Hét annarr Skjöldr en annarr Hjálmr. 
The-one was-called Skjöldr (Shield) but (and) the-other Hjálmr (Helmet)

Konungr hélt mikit af þeim. 
(The) king made much of them (halda, Z.iii).

Ei váru þeir þokkasælir af alþýðu. 
They were not well-beloved of people-in-general (the common people)

Hlégerðr var mikil fyrir sér; konungr var henni eptirlátr. 
Hlégerðr was very powerful; (the) king was indulgent towards her.

Ekki fell mjök á með þeim Ingigerði ok Hlégerði.
Nothing much (pleasant) fell out between them, Ingigerðr and Hlégerðr (ie they were not on good terms, falla, Z11).