The word "nieuwe" on the audio sounds like /neever/ and I don't know if that's good or not.
Yes, that's what I hear with both the male and female voices. There is a clear v sound in the pronunciation. Sounds like Irish Niamh followed by a schwa. However, Forvo is a different story. There we get two clear English w sounds, but slight variations in the vowel sound. One speaker sounds like "neewa", the other like "nyoowa". combinations of nieuwe with other words also show this slight variation, but all have a clear English w sound. I can only conclude that either both Duolingo speakers are getting it wrong, or that the sound reproduction is at fault. I choose the latter. And I'll be saying "nyoowa" until someone corrects me.
We put an "e" at the end the most of the times.
Except for :
-Predicative adjectives. "de nieuwe jongen" but "de jongen is nieuw"
-N.S.I. words: Neuter( words with het), Singular AND Indefinite. "de nieuwe jongen" , "een nieuwe jongen" , "het nieuwe meisje" , "een nieuw meisje" , "de nieuwe meisjes" and "nieuwe meisjes"