The sentence doesn't sound too natural for me in Romanian. I would say it different, it is good just to learn words.
Maybe it refers to "two new kids in your classroom", we use that in Romanian
You are right. A correct expression would be "Voi aveți doi copii nou-născuți”, which would translate "You have two newborn children" or "You have two newborns"
Would the sentence sound more natural if it were about newly adopted children?
Sure, we can say "newly adopted children", but that would translate "copii nou-adoptați”. But in another context we can say ”Voi aveți copii noi la grădiniță”, which would translate ”You have new kids in the kindergarten”.
This could actually be quite useful if I go teach TEFL English in Romania:)
It could be referring to a staff member or whoever telling another person about new students in a class which happens alot (the teacher is new and not aware of the changes). This happened to me in Taiwan where I started a class and was told that some students were new. The change of students was new, and it was my first lesson with that same class.
Is Romanian similar to Spanish in the sense that the adjectives come after the noun? Is that a rule?
It is not necessarily a rule, but it is a very strong tendency for most adjectives, at least. If you put adjectives before a noun it can sound poetic (I would avoid doing that unless you know what you're doing, you can sound ridiculous otherwise). Sometimes the adjective changes meaning depending on whether it is placed at the beginning or the end of the noun. Examples:
Săracul copil nu are prieteni! - The poor kid doesn't have any friends! (Poor him!)
Femeia săracă a trebuit să împrumute bani. - The poor woman had to lend money (she is poor in the literal sense of the word: she does not have money).
mare (big, but also great):
Clădirea (cea)* mare se află pe dreapta. - The big building is on the the right.
Marele nostru lider ține un discurs! - Our great leader is giving a speech! (he is great and mighty and such)
*The sentence sounds more natural with "cea", yet it is not mandatory. Ignore it for now.
Must be something like French where, more or less, after is literal and before is figurative. Pretty much the same in Italian as well.
If I got it right, it's the same in Portuguese. So, adjective after noun must be kinda Romance...
Is the "new" in this sentence a gender-specific adjective like in Spanish? What about quantity specific?
Copii is used for both girls and boys? I mean the child gender won't change the word?
This is a strange statement, even in English one wouldn't say you have two new children. They're not products! Perhaps they were bought from Lidl.
Because this is such a weird sentence in English (but not in a cool, or humorous way) it makes the lesson a bit difficult for the learner. I would reconsider including this one in the series. That said, I flipping LOVE this course and everyone who contributed to it! You guys are awesome!