> og mun þér það minnisamt
> and it must be called to mind

"and [I expect] that will be memorable to you"
MM & HP: "it must still be fresh in your memory"

> Skal eg og aldrei una því að engi komi mannhefnd eftir hann."
> I shall never be satisfied because no blood was shed for him (lit.

no blood comes after him)

"I shall never be content without there being vengeance for him."
"I shall never be happy unless there is vengeance for him."
"I shall never be satisfied unless he's avenged."

Here the pronoun 'því' is the dative object of 'una' "to be content",
rather than serving as a conjunction "because". It correlates with the
subordinate clause 'að engi komi mannhefnd eftir hann' "that there
come not vengeance after him [being dead] (i.e. for his death)."

'Skal eg og aldrei una því'
"I shall never be content with that"

Content with what?

'að engi komi mannhefnd eftir hann'
"[with the eventuality] that no vengeance should come for his death."

Notice that 'komi' is present subjunctive; it's the possibility of
vengeance not coming that he's saying he'll never be happy with, if
such a possibility comes to pass, rather than saying that he'll never
be happy now because no vengeance has been taken yet.