The answer to many of your questions is "Yes, with qualifications and probably not the way you're thinking of, if you're using movies as your reference".
In movies, the heroes take on 3 guys coming from different directions without any problem - they turn at just the right time, or maybe they throw a backhand or rear kick, they duck the attack coming from behind... because it's all scripted. In reality, you have to really struggle not to go into tunnel vision when the adrenaline hits, and it becomes very easy to focus on the person in front of you and not pay attention to the fact other people might run up behind you. This kind of sucker punch scenario happens A LOT.
In the movies, people don't get tired until the very end of the fight, if at all, and then they find a second wind and do the most amazing moves ever. In reality, unless you spend a lot of time conditioning, you're probably going to get tired quick and get sloppy. While this also applies to your opponents, if there's more of them than you, they're splitting up the energy cost, while you have to stay "on" the whole time. This is pretty much the classic hunting strategy from the days when we hunted with spears - wear down the prey, take turns, catch your breath.
In the movies, heroes come back from injuries a lot. Or things that should injure them, don't. You're not going to take hits from a baseball bat and "be ok", you're not going to take multiple kicks to the ribs and head while you're on the ground then magically come back and win the fight.
Not getting injured in the first place is a high priority in reality.
The best part of movies is stuff like spinning flying jump kicks and all that cool stuff. It's not that none of these EVER work, it's just that either you have to have surprise, have set up a bunch of things first to get to do the move, and finally, odds are, you'd be safer doing something simpler.
I know one person who successfully did a jump kick in a brawl in high school. He hit the guy by surprise, hit him in the jaw and clean knocked him out. That was the one flashy move of that entire fight - he didn't go around jump kicking everyone else.
Tripping and Falling
In the movies, people only fall down when they get thrown. In reality, people trip and fall over everything. The world is a messy place, and unless you're in a nice, flat area that has a lot of space like a competition ring, you might find yourself tripping or backed up against stuff all the time.
Depending on how you've trained, you can use the environment to really help deal with multiple opponents- preventing them from all coming at once, tripping or knocking them over in a way that will take more of their time getting up, or hurting them in the process.
Real World Stuff
Do you need a Black Belt? A black belt is a form of rank, and originally it just meant you got the solid basics down, not "mastery". So, in a sense, yes, if you're going to take on multiple opponents or weapons, in whatever style you study you better damn well have gotten your foundation work together. The belt has jack to do with it as much as the training you put in.
A lot of styles DO train to take on multiple opponents, but as much as anything, some are more realistic and better at real world fighting, others not so much. That endurance and awareness issues I brought up before play a big part in this.
Mostly the places where we see people successfully take on multiple opponents? The singular person is someone with a ton of conditioning and fitness plus a lot of training and the multiple opponents don't have it.
Weapons are dangerous and deadly. And if you don't have a weapon and someone does, you're at a major disadvantage. People can and have disarmed folks before, but you don't want to stay unarmed in a fight with weapons.
I've seen footage of people fending off knife attacks by taking their shoes off and putting their hands in their shoes as arm guards, just to get something to block with. Weapons make things desperate and scary and it's not like the movies where a knife cut is a small red line across your arm...
What style will help?
There's no one style that will make you a super warrior, otherwise everyone would do it. There's different styles that focus on different things, and within those styles, different schools and teachers.
In general, you want a style that:
a) gives some form of live partner training (sparring, high end drills, etc.)
b) teaches you to deal with multiple opponents
c) teachers you to deal with weapons
You'll want to do a ton of conditioning as well.