> að heimboði
> a home-feast (?)

Yes, for a visit such as would typically involve a feast.

> "að stórvandræði leiði af."
> "that great trouble will lead from it"

"[...] will result from [it]."

> hinn þriðji mestur lögmaður á Íslandi.
> he was third (?one of three) most/greatest lawyers in Iceland

Specifically "the third greatest". You might be thinking of the idiom
'einn hinn mesti' "one of the greatest".

> óþykkt
> ?coldness?

Yeah, discord, disagreement, falling out. Compare 'samþykkt', f.
(='samþykki', n.) "accord, assent, agreement", 'samþykkja' "to
consent; reconcile", 'þykkja' "thought, disposition, sentiment;
dislike, displeasure", 'þykkjask' "take offence", 'þykkjulauss'
"good-natured, easy-going", etc.

> harðger
> ?resulute?

MM & HP: "a man of great vital energy and COURAGE". Here is an example
of the word translated as "firm" [
http://digicoll.library.wisc.edu/cgi-bin/IcelOnline/IcelOnline-idx?type=HTML&rgn=DIV1&byte=175731
]. Zoega has "hardy, stout". Fritzner equates it with 'harðfengr', for
which Zoega has "hardy, valiant". (When used of inanimate objects, it
means simply hard or sturdy.)