Sorry for a late reply - it has been a very busy week, culminating in last night’s launch party for my first album of my original songs. I also apologize for a long, rambling answer. If brevity is the soul of wit, I am an inanimate object…
Wow, that’s more than just ‘A’ question! 
I’m flattered by your interest!
how exactly does one become a professional opera singer in this day and age?
The answers there are as varied as the individual singers. I’m going to stick to the Canadian scene, because that’s what I’m most familiar with… Juan Chioran and Roger Honeywell both started out as actors, and side-stepped to opera when they took singing lessons and found out they a) liked it, and b) were pretty good. Brett Polegato is someone who, as far as I know, always wanted to be an opera singer. Rihab Chaieb was a singer in a heavy metal band who took some lessons when her voice was getting tired too easily, and found out she was good at it… The list goes on - many different paths to (and away from) opera.
It certainly doesn’t seem like an occupation one ends up in on accident, and I assume there’s probably a lot of very specific physical training that goes into being able to project your voice clearly and with proper intonation. Is it something you decide on when you’re a kid, or is that a decision that gets made later on?
In my case, it was an accident. I don’t remember when I started singing - I think I would have been 5 or 6 years old when I was in the junior choir at the Presbyterian church where my parents were both elders. From there, I had a typical path for a kid interested in music growing up in the 60s/70s - recorder in Grade 4, trumpet in Grade 5, switched to tuba in Grade 7. Grade 7 was when I first heard Mike Oldfield’s “Tubular Bells”, and that was a life-changing album for me. Guitar in Grade 8, along with continuing to listen to every jazz, rock, fusion, folk album I could find. By Grade 10, I wanted to be the next Zappa, or Mahavishnu John McLaughlin, or Steve Howe (Yes), or Steve Hackett (Genesis), or - you get the drift. Meanwhile, I’ve gone up into the intermediate choir, plus the senior choir, at church, and into our high school choir. Then throw in the high school concert band, the stage band, and various bands we put together to jam.
(A topic for another thread, but I mourn for kids in contemporary public school systems, where choirs and bands are vanishingly rare. And the decline of churches mean that those church choir opportunities are also disappearing. Private schools in Canada all sell themselves based on their music programs, but talent knows no socio-economic categories.)
End of Grade 12 - I barely got out of High School. If it wasn’t music, if it wasn’t written by Asimov, Clarke, or Tolkien, if it couldn’t be used in a D&D game, I wasn’t into it. I wanted to go to university, because everyone I admired had some serious theory, history of music, composition chops in addition to their skills on their instruments, but - with a 52 in English, the Berkeley/Berklee schools were right out. So was anything else out of country or out of province. Fortunately, my home town (Brandon, Manitoba) had a university with a very good music faculty (Have you heard of the violinist James Ehnes? His father was one of my profs…) and, most importantly, a certain obligation to take a number of ‘local losers’. However, you couldn’t just be a theory/comp major; you had to have a major instrument or be a voice major. There was no stream for jazz/rock guitar, I didn’t play classical guitar, I didn’t really want to be a tuba major, so I fell back on my choral singing and auditioned as a voice major.
2 years later, my teacher is saying to me “You might want to audition around a bit; your voice has really come along, I know from your roommate that your guitar hasn’t been out of its case in months, and who knows? You might get something!” So I auditioned for the Banff School of Fine Arts (as it was called at the time), got into a summer opera program, and I loved it! Got back from the summer, got a call from Edmonton Opera - would I like to do a school tour of HMS Pinafore, along with Hansel and Gretel and La Boheme, along with being a section lead/doing small roles in the manstage shows? So, I went out there and toured for 9 1/2 months. That was the start of my career, in 1982. (Sadly, those kinds of opportunities don’t exist any more - there are programs for young singers, but they’re not extensive like the ones back then.)
Is there a college major in opera performance, or certain types of schools that specialize in opera?
Yeah, it tends to be based in university music departments. A very typical path right now is to get a B. Mus. in voice, and move on to a M. Mus. or graduate diploma, possibly followed by a Doctorate. By the Masters level, students will get some training in acting, dancing, stage combat, and will get some practical experience in fully staged opera productions. University of Toronto, McGill University (Montréal), University of British Columbia (Vancouver) all have extensive voice departments/opera programs. I know these can be found throughout the US as well, but I don’t know a lot of particulars - Julliard, Manhattan School of Music, University of Michigan all have faculties that have produced singers that I’ve been lucky enough to perform with.
However, like any other of the performing arts, the degree is not necessary - what counts is how well you perform. I, myself, have never graduated.
What’s the audition process like?
The first trick is getting the audition - if you don’t have an agent, you might find it a real challenge to get an audition at all. Most companies will have a chorus, and if they’ve never heard of you and you don’t have much on your resume, you may be able to get into the chorus. Singers in the chorus may be purely volunteers, they may receive an honorarium, or it can a quite lucrative position. The full time chorus at The Met makes something like $100,000.00 + per year, but it’s also a full-time commitment - 6 days a week from late August until late June, most days are at least 2 session days, some days are 3 session days.
Typical audition, once you get it - you offer to sing 5 different contrasting arias. You pick what you start with, they get to pick the second. Sometimes, you might be asked to sing a third. More than that is pretty rare, and quite taxing. From there, it’s down to them to decide if they’ll offer you anything. You need to get used to rejection - 1 gig out of 10 auditions is a very good success rate. Also, just because they didn’t take you for next year’s season (the time line on opera is insane! This year’s season is already booked and in place, barring replacements. They’re looking to future seasons - the highest paid stars are booked 2 - 3 years in advance!), it doesn’t mean they’re not considering you for further up the road.
Are you expected to be fluent or semi-fluent with the languages you sing?
At very least, you’re expected to know what you’re singing, and what other characters are saying to you. You need to pass for a native speaker, so your accent must be minimal in the target language. It’s possible to perform by learning your part phonetically and knowing a translation, but I don’t recommend it. I’m lucky - I have an affinity for learning languages, and I find it easier to just learn the rudiments and go from there. It’s actually our privilege to learn another language through its song - most people learn from speaking or reading; the combination of poetry and song is a magical way to learn! (It also has its hazards - the language of opera tends to be heightened, and can be archaic. Picture someone who learned their English through Shakespeare, and you get an idea of how we sometimes sound at the Italian grocery store…)
Consider as well - your colleagues may be from all over, you may be working all over, and it’s a respectful gesture to be able to communicate in their language. Or the language of the country where you’re working.
Are there certain performers who are considered to be like the rock stars of the opera world who can sell tickets to a show because their name is on the bill?
There are a few that come to mind - Joyce DiDonato, Sondra Radvanovski, Emily d’Angelo - but we don’t have anyone right now that would be a household name like Pavarotti was in his day. Certain opera houses, like The Met, just have a reputation for hiring the very best performers they can find, so while the aficionados may debate whether they’d rather hear Thomas Hampson or Gerald Finley in role X, many people who go to The Met or The Met in cinemas are just expecting that who they hear that evening is one of the best people possible for that role.
You might be interested in this thread from 2008 - I haven’t run into either @figaro or @fachverwirrt for a while, and I’m not sure if they’re still on the SDMB, but I’m still here. Have a look at Ask the Opera Singer(s)...