There is no fűv.
There is only fű, which has two stems, fű- and füv-; case endings are added sometimes to one stem, sometimes to the other, depending on the case. (Note that the füv- stem has a short vowel.)
Similar two-stem words include ló, lov- "horse" and kő, köv- "stone".
I think that the -v- was originally part of the word but fell off when it was at the end or before a consonant (but lengthening the vowel in compensation) while remaining between vowels (i.e. when the case or number ending started with a vowel). Compare, for example, Finnish kivi "stone" with -v-.
'Bunnies' or 'Bunny' would be a very childish way of speaking in English, Two adults talking together would tend to use 'Rabbit/s' I'd guess that 'nyuszik' doesn't sound so childish in Hungarian, maybe the kindergarten teachers would know!
I think "nyuszi" is actually relatively childish, or at least endearing. One would mostly say it to a child, or use it when referring to those sweet little balls of fur.
It is not easy to put a number on the level of childishness though.
How do I know to include the "the" in this English sentence? In other Hungarian sentences with "a" the English word "the" is not included but in this English sentence it is. Why? The sentence makes sense in English both with and without the "the"
I think "Bunnies play on the green grass" could be a translation of this sentence but not "Bunnies are playing on the green grass".
If "a X gets translated as "X" in English without the "the", it's talking about generalisms ("lions are carnivores"), as I understand it.
But "bunnies (in general) are playing" sounds wrong to me as a translation of Duolingo's sentence with a nyuszik - if you are talking about bunnies in general, you would say what they do in general: using the present simple for habitual situations.
"are playing" is something that is happening now, and then you know what is doing it: some bunnies that you see.
I think that would not be the sort of thing covered by generalised a nyuszik.
Yes, I think the two best translations would be:
"The bunnies are playing on the green grass."
"Bunnies play on the green grass."
But then what about the situation when you look out of your window in the morning and see bunnies playing on the green grass? They are not "the bunnies", because they are not yours and you have never seen them before. But it is happening now. What is the correct way of saying this? You just stick something in front of "bunnies", other than "the"?
"Some bunnies are playing on the green grass."
"There are bunnies playing on the green grass."
"I see bunnies playing on the green grass."
So you can't just say "Bunnies are playing on the green grass"?
A good Hungarian sentence for this situation would be:
"Nyuszik játszanak a zöld füvön".
"Bunnies are playing on the green grass." is a perfect English sentence for your situation.
I just didn't think that it was a good translation of A nyuszik a zöld füvön játszanak. with a nyuszik. I've updated my previous comment to be a bit clearer.
(And I'm glad to hear that Hungarian would omit the article in this context, confirming my suspicion)
Your three English suggestions are also possible.
Yes, both versions should be accepted. If they are not, please report them (Report a problem) so the course creators can fix the issue. Thanks.