> skörungur
> very noble

I think the noun describes someone with fine personal qualities: "an
outstanding/remarkable/impressive person", rather than being noble in
the sense of having "noble birth".

> Bishop Bjarni (?Bjorn)

'Bjarnar' is the genitive of Björn (declined like 'skjöldr', except
that the nominative 'r' has been assimilated to the preceding 'n'), thus:

Björn - nom.
Björn - acc.
Bjarnar - gen.
Birni - dat.

'Bjarni' is a weak masculine noun, so:

Bjarni - nom.
Bjarna - acc.
Bjarna - gen.
Bjarna - dat.

Congratulations on finishing the translation! Good work, both of you.