> Þá sér hann kerru Þórs og tekur af honum annan gullhring.
> He then saw Thor in his chariot and took another gold ring.

More literally: "Then he sees Thor's charriot/wain and takes another
(a second) gold(en) ring off him."

> Tók þá að morgna.
> It took then to morning (?) (Dawn was breaking)

You could maybe paraphrase as: "It began to get light."

> akurland
> cornfield

Okay, with the proviso that Eysteinn made a while back about how
"corn" can mean different things in different parts of the English
speaking world...

> en særir Þránd til ólífis
> and wounded Thrand badly

"and mortally wounded Thrand"

> "Kosti á eg nú að vega þig og vil eg það eigi. Skal eg meira virða
mágsemd við þig en þér virðið við mig."
> "I could (have the choice) to kill you now but I shall not. I shall
have more value/respect for my relatives than you have for me "

Yes: "I could kill you", "I have the option to kill you", "it's in my
power to kill you". 'mágsemd' is literally "the relationship of being
a male inlaw", but that's a bit of a mouthful, so some some
paraphrase, such as you've made, would be reasonable in an idiomatic
English translation. MM & HP have "family ties" which doesn't stray
far from the original and preserves Hrapp's cheek! 'kosti' is the
accusative plural of 'kostr', compare the examples quoted by Zoega:
'eiga alls kosti við e-n' "to have someone completely in one's power."