Here’s my translation

Alan

Meykóngur tók nú einn náttúrustein og brá yfir skipið og höfuð þeim öllum er innan borðs voru. 
[The] maiden-king took now one magic-endowed-stone and quickly-swept [it] over the-ship and [the] heads of all those who were on-board.

Sá jarl þau aldri síðan, en þau meykóngur og Hléskjöldur halda fram ferðinni, léttandi ei fyrr en þau koma heim á Pul. 
[The] ‘earl’ saw them never after-that, but (and) they, [the] maiden-king and Hljéskjöldr, held [course] (continued, maintained) forward the-journey, stopping not before they come home to Púll (Apulia).

Gengur frú Egidía móti þeim með miklum prís og fagnaði. 
Lady Egidía goes (on foot) towards them with great pomp and welcoming-joy.

Situr nú meykóngur þar um hríð. 
[The] maiden-king now remains (lit: sits) there a while.

Síðan lætur hún búa sína ferð og skipastól heim til Frakklands, beiðandi frú Egidía að Hléskjöldur hennar son fylgdi henni að styrkja hennar ríki fyrir áhlaupum hermanna. 
After-that she-causes (<láta>, Z5) to make-ready (for) her journey and [her] fleet-of-ships home to France, asking Lady Egidía (presumably, this is the accusative?) that Hléskjöldr her (Egidía’s) son accompany her (Nítíða) to strengthen her kingdom against (in the face of) [the] attacks of men-of-war.

Hennar fóstur-móður veitir henni þetta sæmilega, sem allt annat það er hún beiði, út leiðandi hana með fögrum fégjöfum og ágætum dýrgripum í gulli og gimsteinum og dýrum vefjum. 
Her foster mother grants her this honourably, as all other [things] that which she (Nítíða) requested, leading her out with fine gifts-of-money and excellent things-of-great-value in gold and gemstones and costly woven-cloths.

Skilst þessi hoflýður með miklum kærleik. 
These courtly-folk (people of the court, nobility) part-company with great friendliness.

Siglir meykóngur í sitt ríki með miklum heiður og veraldlegri mekt. 
[The] maiden-king sails to her kingdom with great honour and worldly might.

Verður allur lands-lýður henni feginn stýrandi sínu ríki með friði og náðum. 
All inhabitants-of-the-land become (ie are) glad of her, governing (lit: steering) her kingdom with love and mercy.

II 
11

Hugon er kóngur nefndur; hann réð fyrir Miklagarði. 
[There) is a king named Hugon; he ruled over Constantinople (lit: Great-City).

Hann átti drottning og tvö börn. 
He had a queen and two children.

Son hans hét Ingi; hann var allra manna sæmilegastur og best að íþróttum búinn. 
His son was-called Ingi; he was of all persons (men) most-becoming and best endowed with accomplishments (skills).

Hann lá í hernaði hvert sumar og aflaði sér svo fjár og frægðar; drap ránsmenn og víkinga, en lét friðmenn fara í náðum. 
He was-engaged in warfare each summer and gained for himself thus wealth and renown; killed robbers and Vikings, but allowed peaceful-persons (men) to travel in peace.

Listalín hét dóttir hans; hún var fríð sýnum og vinsæl, og hlaðin kvenlegum listum. 
His (King Hugon’s) daughter was-called Listalínæ she was beautiful in appearance and popular, and laden (loaded) with womanly skills

Soldán hét kóngur; hann réð fyrir Serklandi. 
[There] was a king called Soldán; he ruled over Serkland (the land of the Saracens)

Hann átti þrjá sonu: hét einn Logi, annar Vélogi, þriðjungur Heiðarlogi—hann var þeirra elstur. 
He had three sons: one was-called Logi, [the] second Vélogi, [the] third Heiðarlogi – he was [the] eldest of them.

Hann hafði svart hár og skegg. 
He had black hair and beard (not sure if this means his beard was also black, or just that he had a beard).

Hann var hökulangur og vangasvangur, skakktentur og skjöpulmyntur, og út-skeifur. 
He was long-of-chin and thin-of-upper-cheek (<vangi> + <svangr>, thin, CV), wry-toothed (CV) and twisted-mouthed (<mynntr>, part, mouthed CV + based on what I found here: https://malid.is/leit/skjapp and see also <skjöplast>, to make a mistake, MnI) and ‘knocked-kneed’ (latin: <valgus>, see under <skeifr>, CV).

Annað auga hans horfði á bast en annað á kvist. 
One eye of his turned-so-as-to-look-on [the] cord/binding (or inner bark) (ie ‘inwards’) and [the] other to [the] twig (or outer branch) (ie ‘outwards’)(as with McDonald my immediate thought was one eye looked inwards, the other outwards, but couldn´t find anything to directly support this).

Hann var hermaður allmikill, og fullur upp af göldrum og gerningum og rammur að afli, og fékk sigur í hverri orrostu. 
He was a very great warrior, and full up of (ie fully versed in) sorcery and wizardry and strong of physical strength, and obtained victory in every battle.

Bræður hans, Logi og Vélogi, voru vænir og gildir menn og herjuðu öllum sumrum. 
His brothers, Logi and Vélogi, were handsome and worthy persons (men) and went-freebooting all summers.

Blebarnius er kóngur nefndur; hann réð fyrir Indíalandi hinu mikla. 
[There] is a king named Blebarnius; he ruled over India the great.

Hann átti son er Liforinus hét; hann var væn að áliti, ljós og rjóður í andliti snareygður sem valur, hrokkinnhærður og fagurt hárið, herðabreiður en keikur á bringuna, kurteis, sterkur og stórmannlegur. 
He had a son who was-called Liforinus; he was handsome in appearance, fair and ruddy in countenance, keen-eyed like a hawk, curly-haired and the-hair fair, broad-of-shoulder but (and) bent-backwards in the chest (ie his posture was such that he leaned slightly back, very upright, rather than being hunched over, see <keikr>, CV), well-bred, strong and like-a-great-man.