Should i attend the New York Film Academy?
NYFA is a for-profit diploma mill. As far as I recall most of the student body is international - because it is easier to get into. Once you finish the program, you will still have a high school diploma, living in one of the most expensive cities in the world. Washington Heights is cheap, but gentrifying quickly. So is Brooklyn - besides the incredibly dicey neighborhoods nearly anything within a couple stops' distance from Manhattan is prohibitively expensive. What are you plans after that? NYC has no shortage of starving artists - only that many of them will have advanced degrees with school connections from NYU, Pratt, FIT... If you're intent on doing this conservatory program and live anywhere near the city I would strongly suggest you commute. NJT will drop you off at Penn Station and it is one stop on the Broadway express to Union Square. My advice: if you are set on an arts program, get the degree, it's certainly better than a certificate and the bachelor's will help you get your foot in the door to most any job.
Bachelors of Arts in Music or a Bachelors in Music?
It is VERY unlikely that your daughter will be able to make a career as an opera singer. Actually, we could say that about virtually anyone. The odds are simply stacked against any young person wating an operatic career, because there are not that many jobs available, and there are very many people who would love to have them. That's the first thing to be aware of. The second thing to understand is that the competition consists of young people who have excellent and well-trained voices, and who have been through a top opera programme, for example studying at the Juliard, or one of the four or five conservatories in the US which might be roughly equivalent, or in Paris, Vienna, or nowadays Beijing of Seoul. This is a global profession. The third thing, and by the sounds of it the most critical in your daughter's case, is that the few who do make it generally have THREE things going for them. A good natural voice, an excellent education, and single-minded determination. If that last is missing, now is a good time to give up. If it isn't there, she won't make it. And although you can provide encouragement, you can't give determination. There is one other thing which might possibly be relevant. You don't say what your daughter's Fach is, as far as I remember from the question. There is more competition in some areas than others. If she is a lyric soprano, then those are six a penny throughout the world, so that would be bad news. On the other real contraltos or dramatic sopranos are rather rarer. Quite a lot rarer, in fact. Check what she is, and bear this in mind. But barring a really unusual Fach, it sounds to me to be time for Plan B. Sorry.