Translation:I live in Italy, because it is such a beautiful country.
No, "...so beautiful country" should not be accepted. If you take "niin kaunis" by itself, you are right, it will translate to "so beautiful." If you put the subject first with no predicate noun it works, e.g. "Italia on niin kaunis" = "Italy is so beautiful."
But before nouns we need to use "such a." Here, have a look at this: https://www.perfect-english-grammar.com/so-and-such.html
I don't think so. In a sentence like 'Se juo ja syö täällä', you don't need a noun before the second verb because it has the same subject as the first verb.
In the first clause here, 'Asun Italiassa', the subject is an implied minä. In the second clause introduced by koska, we're now talking about Italy.
And unlike ja and mutta, I'm not sure you could omit even a repeated subject with the subordinating conjunction koska.
Duolingo doesn't seem to like any contractions involving an apostrophe followed by 's'. I've seen complaints about Duolingo wrongly marking contractions as typos from people doing other language courses as well.
Unfortunately, I'm pretty sure our moderators don't have the ability to do anything about it.