Could I say, "Jeg begynner å kjenne Norsk," in order to mean that I am beginning to understand the Norwegian language?
You could, but it sounds a little strange. It's better to say " Jeg begynner å kunne prate norsk."
"Jeg kan litt norsk."
If you go to Norway after finishing this course, say this sentence.
Then, after a while they will understand that you speak Norwegian.
I am sure you can say both "ham" and "han" here
Some history on the subject (alas in Norwegian).
For people on mobile devices sometimes the links need to be typed out:
http://www.sprakradet.no/Vi-og-vart/Publikasjoner/Spraaknytt/Arkivet/Spraknytt-2008/Spraknytt-22008/Spoersmaal-og-svar/
The very fact this this is over my head makes me excited to try to read it. Takk!
I want to make sure that I'm understanding a key point here correctly: In old Norse, the accusative and nominative come from "hann", and "ham" is actually originally dative?
a very helpful link, which also clarifies all other questions you might have:
https://www.duolingo.com/comment/8777724
You deserve so many thanks and hundreds of Lingots!
Correct