Here’s my translation

Alan

Nú fréttast þessi tíðindi víða, ok þykir mönnum mikils um vert. 
Now these tidings became-known widely, and (it) seems to people (men) worthy of much (attention) (ie people thought it a very big deal).

Þótti mörgum góðr kostr þar sem Ingigerðr var, ok því réðu til ágætir menn at biðja hennar, en þat fórst öllum einn veg því hon lét alla drepa, ok binda höfuð þeira við garðstaura. 
(It) seemed to many (people) a good match (kostr, Z4, choice in marriage) there where Ingigerðr was (ie when it came to Ingigerðr), and therefore excellent (highly-credentialled) people (men) attempted (ráða til, Z16) to ask for her (in marriage), but that went (ie turned-out, farast, Z11) one way for (them) all, because she caused to kill (them) all, and (caused) to bind their heads against fence-stakes (acc plural).

En þeir menn sem sér tóku vetrvist hjá henni þá forréð hon alla, en tók fé þeira til sín. 
But those people (men) who took for themselves winter-abode with her, she betrayed (for-ráða, CV) them all, and took their wealth to herself.

Varð hon af þessu víðfræg en ei vinsæl, ok þótti mönnum þetta mikil vandræði. 
She became famous from this but (and) not popular, and this seemed to people (men) a great difficulty.

Hon gaf sér ei mikit at þessu, ok helt uppteknum hætti.
She gave to herself not much (notice) on this (ie she cared not one whit about it), and maintained the-seizures (of wealth, see two lines above) (upptaka) as usual (dative of háttur) (this reading seems to me just as valid as ‘to go on in one’s usual way’, háttr, Z1)

Hon var á flesta hannyrði mjök kæn, ok barst þat víða, ok þótti því mörgum fýsiligt at fá hennar ef þess yrði auðit, stóð nú svá mikill ótti af hennar tiltektum at engi vágaði hennar at biðja, eðr nökkur viðskipti við hana at eiga, ok fór svá fram um hennar ráð, þangat til sem hon hafði þrjá vetr um tvítögt.
She was very expert in most fine-work, and that was-born (ie reported) widely, and (it) seemed therefore to many (people) desirable to win her (ie her love, fá, Z3) if (it) became destined for that (ie if that fell to one´s lot), (‘although’, there seems to be a conjunction missing here) such great dread of her modus-operandi now existed (lit: stood) that no-one dared to ask for her (in marriage), or to have any dealings with her, and (it) went thus forward concerning her rule (ráð, Z6) (ie her rule continued in such a manner), until-that-time that she had about twenty-three winters (years) (until she was about 23 years old)

4.
(Chapter) 4

Tókum nú þar til máls sem Sigrgarðr er í hernaði. 
(We) take now (the) story to there (ie to that point) where Sigrgarðr is a-harrying.

Honum varð gott til fjár ok mannorðs. 
(It) became good for him in wealth and fame (ie he prospered in wealth and fame).

Hafði hann þá aukit mikit um fjölmenni sitt; hafði hann nú fengit tíu skip skipuð með góðum drengjum. 
He had then (ie by that time) greatly increased concerning his many-people (men) (ie augmented his following); he had now gotten ten ships manned with good men-of-valour.

Hann var frægr af sínum hernaði, en sömu hélt hann í fram um kvennafarit.
He was famous for his harrying, but (and) he kept forward (continued) in the same (way) concerning the-going-after-women (womanising).

Hann hefr nú frétt af meykonunginum í Tartaría ok fannst honum mikit um. 
He has now intelligence of the-maiden-king in Tartaría and (it) pleased him greatly concerning (it).

Sét hafði hann margar hannyrðir þær sem meykonungrinn hafði gjört, ok þótti jafnt vera sem fölski allt þat sem aðrar gjörðu hjá því sem hon gjörði, en nú með því at hann treystir sér vel ok þóttist ei minna verðr eðr enn nökkuru framar enn þeir aðrir sem hennar höfðu beðit þá býr hann ferð sína austr í Tartaría.
He had seen those many fine-works which the-maiden-king had made, and all that which others made seemed to be just like white-ashes by (ie when compared with) those which she made, but (and) now with that that (ie because) he trusted to himself well (ie was confident in his own abilities) and bethought-himself not worthy of less (ie not inferior) or yet somewhat more-advanced (ie superior) than those others who had asked for her (in marriage, pp of biðja), then he makes-ready-for his journey east to Tartaría.,

En er hann kom fyrir hafnir þær er lágu fyrir borg meykonungsins hagaði hann svá siglingu sinni at þeim skyldi sem mest tilsýnast ok tilfinnast er fyrir váru.
But (And) when he comes before those havens (plural) which lay before the-maiden-king’s castle he arranges his sailing such that (it) should most be-favourable (sýnast til) and be-pleasing (finnast til) to those who were in-front (of him).