I had a cheesy college professor who always used to say "the only dumb questions are the unasked one's"....debatable, perhaps, but still....suck it up Duolingo!! ;)
What's the difference between 'stiller' and 'spørre'? Are they synonyms or they are used in different contexts or...?
You "stiller et spørsmål", but "spør" about something.
You can think of "å stille" as "to pose (a question)" if that helps, though the usage is a bit more limited in English.
Every time I see the word "spør", my brain autocorrects it to "SPQR". Ave Cæsar!
No, 'stiller' is the present tense of 'stille', so it's the same no matter how many people are doing it (eg, 'jeg liker' and 'de liker' are the same, etc).
Would it be weird to say "De sporrer sporsmal"? (Sorry, can't type the special characters on this keyboard.)
In that case: De spør spørsmål. (Not spørrer). But it is a bit weird. It will be like saying I'm going to run for a run (when you are actually just going to exercise and do it by running).
To ask a question = å stille et spørsmål = å spørre (no need to say it's a question as it's already there in the verb itself).
Yes, you could also say "De spør spørsmål" it is done in many dialects, while in other dialects it might sound a little odd, but still wouldn't be wrong.
In some dialects it would not just sound odd, but childish, to say "De spør spørsmål". A construction like "De spør om..." (translated: "They ask if..." would fit in a lot of situations. I think grydolva is very much to the point here. When you use the verb "å spørre" it is understood that you talk about a question.
And again in others it won't, in Northern Norway this is a common sentence:
"Dæm sporte oss masse spørsmål om jobben våres"
I know, I lived in Troms for nearly 10 years and interacted a lot with people from Nordland, too. Since Duolingo doesn't seem intent on teaching any of the structures most often found in spoken Norwegian, I still think it is good advice to learn the most standard expressions first.