I've found there are enough similarities between Norwegian and Swedish that just by using this course and not studying any Swedish, I'm still able to translate a decent bit of the Swedish music I listen to. If you learn to step back and imagine other ways the word could be said, you can sometimes even find parallels in German and Dutch.
Apparently the 'ni' comes from a contraction of '-(e)n' verb endings to the plural second person pronoun 'i' (originally Old East Norse 'ír'), the equivalent of English 'you'. These became fused together as 'ni'. The same thing happened in Old West Norse (Icelandic and Norwegian) where '-(i)ð' + ér became 'þér'. This same contraction gives us words like apron (an apron < a napron), newt (a newt < an ewt < an eft), adder (nadder) and nickname (ickname).
That's correct, it can be used as "Jeg beklager!", or shortened to just "Beklager!" for a simple "Sorry!".
While it is not implied in the short forms above, nor observed much by the younger generation, there is a distinction between the two which becomes clearer in other settings:
Unnskyld (meg) = Excuse/Forgive me (lit.: absolve me from sin)
(Jeg) beklager = I am sorry (lit.: I express sorrow)