Is it worth learning Norwegian and/or Danish after completing the Swedish tree?
I found it was worth starting them while I was doing the Swedish tree. But everyone is different. What's even more fun is there are other apps where you can learn them from Swedish.
It'd probably strengthen your knowledge of Swedish... Learning similar languages to your target language usually helps you make connections and learn new vocab in your target language. Make sure you're solid on Swedish first (by solid I mean good understanding of all grammatical concepts and pronunciation in the language) because otherwise you might start mixing Norwegian/Danish into your Swedish. I found that after accidentally mixing in Dutch spellings into German, I grew away from it and can keep them very separate.
I'm guessing Norwegian/Danish will have words that are either archaic synonyms or uncommon synonyms to Swedish words, so you'll have multiple words for describing the same thing in Swedish. So I think it'd be beneficial... also if you learn two of the languages, I think you'll be able to understand the third much more easily.
Yes, absolutely. These three languages are pretty similar. Perhaps, it can even strengthen your knowledge of Swedish. But it's totally up to you. Do what you think is the best for you.
Learn Danish, then you pronounce the Danish in Swedish and you've already learned Norwegian :Þ
In all seriousness, do what you want, I'm probably going to do Swedish when I'm done with Danish.
It is up to you! I would make sure you are comfortable with Swedish first. I am redoing the Swedish tree as well as studying it outside of Duolingo, and I waited until halfway through the tree the second time around to start the Norwegian, than half way through that to start Danish. You will find that you already know quite a bit!. However, the three different ways to spell and pronounce the same word may trip you up. If you are easily confused, I wouldn't recommend doing the other two, at least for awhile.
That's probably the best advice when it comes to deciding what languges to learn.
Indeed. If you reach a good listening proficiency with Swedish, you can probably understand at the very least some Norwegian. Danish is harder though.
Personally I think it makes it harder to learn when the languages are too close together because your memory seems to fill in the gaps with the other language until you forget which one you are speaking, but that's been my experience.