> og fóru nær Hlíðarenda er morgna tók.
> and went to Hliðarend when morning came.

Yes. They "went near", "came near", "were approaching H. when it
began to get light." For this use of 'taka', see Zoega 7 + inf. "to
begin". 'morgna' is here the infinitive of the verb 'morgna' (að) "to
dawn, become morning."

> og ætluðu til stóðhrossa.
> and intended to (look for - see to ) a Studhorse

> Þeir leita stóðhestsins
> They saw the Stallion

'leita' + gen. "look for", "search for" (present).

Stud horses, genitive plural.

> meðal lækja tveggja
> between two brooks

That's right. The preposition 'meðal' takes genitive.

> og kváðust sjá hann
> and declared themselves able to see him

Yes, lit. "they declared themselves to see him", i.e. "they said they
could see him".

> Þykir mér það karlmannlegt.
> I think to myself that is a man's work. (i.e. not the job for a boy)

Yes, I think that's the idea, lit. "that seems to me (a) manly
(undertaking)", or you could just say "I think that's a man's work."
Since the dative 'mér' is required by the grammar to show who is
thinking (or who it seems that way to), it fulfills the role of 'I' in
the "I think", if you translate it that way. I hope that makes
sense,so "I think to myself" might be adding extra emphasis not
present in the original. Does that make sense?

> og festi sverðið í skildinum.
> stuck fast the sword into the shield

"and the sword stuck fast in the shield." See Zoega 6 'festa'
impersonal, with accusative 'sverðit'.

Re. 'Rimmugýgr', axes were typically called witch/hag/ogre in kennings.

LN