it could also be said like that:
''hayır, yağmur yağmıyor, kar yağıyor''
and that would be the exact translation of the 'translated english sentence'' :)
in this sentence, since the two verbs are the same verb that is 'yapmak' you can use değil instead of the negated one. it is same for the below example.
Ahmet gelmiyor, Ali geliyor = Ahmet değil Ali geliyor = Ahmet is not coming Ali is coming
In terms of pronunciation, can the word "değil" always be pronounced like "de-il"?
It is actually pronounced like this in PURE Turkish. This "yumusak g" is used to connect two vowels and it is not pronounced, but different accents say it differently. Some say it de-il and some also say it deel!