While things like merging movements and so on is part of the story, it's not the whole story.
You see, by saying "traffic jams are caused by merging mistakes and so on" it kinda implies that if everyone drove perfectly a highway lane could carry infinitely many cars. In actually a highway lane has a finite capacity determined by the length of the vehicles traveling on it, the length of the gap between them (indirectly determined by how fast they can start and stop), and the speed they're moving.
There are finite limits for gap widths and speed determined by physics and geometry. As the system approaches these limits it becomes less and less able to deal with small disruptions. In other words, as more cars move on a freeway a traffic jam becomes more and more likely. The small disruption which is perceived as the cause was really just the nucleation point for a phase change that the system was already poised to transition through. If it wasn't that event then something else would trigger it.
It is interesting to note that once a highway has transitioned from smooth flow to traffic jam its capacity is massively reduced, which you can see in the graphs in the above link. Another interesting thing to note is that the speed vs volume graph, if you flip it upside down, resembles a cost / demand curve from economics, where volume is the demand and time spent commuting (the inverse of speed) is cost. If you do this you see something quite odd, which is that the curve curls up around itself and goes backwards.
This is less like a normal economic situation (the more people use a resource the more they have to pay, the less people use it the less they have to pay) and more like a massively multiplayer version of the prisoner's dilemma. For awhile the cost increases only slightly with growing demand, until a certain threshold where each additional actor making a transaction has a chance to massively increase the cost for everyone, even if consumption is reduced. Actors can choose to voluntarily pay a higher time cost (wait before getting on the freeway) to avoid this, but again, it's the prisoners dilemma. People can just go, trigger a traffic jam anyway, and you'll still have to sit through it + all the time you waited trying to prevent it.
Self driving cars are often described as a way to eliminate traffic jams, but they don't change this fundamental property of how roadways work. It's true that capacity could potentially be increased somewhat by decreasing the gap between cars, since machines have faster reflexes than humans (though I'm skeptical of how much the gap can really be decreased; is every car going to weigh the same at all times? Is every car going to have tires and brakes in identical conditions? Is the condition of the asphalt going to be identical at all times and across every part of the roadway? All of these things imply a great deal of variability in stopping distance, which implies a wide safety gap.), but the prisoner's dilemma problem remains. The biggest thing that self driving cars could actually do to alleviate traffic jams would be to not enter a highway until traffic volumes were at a safe level. This can also be accomplished with a traffic volume sensor and a stop light on highway on-ramps.
Of course trains, on top of having a way higher capacity than a highway lane, don't suffer from any of this prisoner's dilemma stuff. If a train car is full and you have to wait for the next one that's equivalent to being stopped at a highway on ramp. People can't force their way into a train and make it run slower for everyone (well, unless they do something really crazy like stand in the door and stop the train from leaving).
Absolutely. The fact that 3 million people pass through Shinjuku station every day is a testament to that.
If all of those people lived in a city in the US it would be the country's third largest, behind NY and LA. (If we're going by the entire urban area instead of just within city limits it would be the 20th, just ahead of the Baltimore-Columbia-Towson metropolitan statistical area.)
All in a space that's smaller than most highway interchanges.
And that's not even using two-level train cars (which is where your figure for 360 people per train car comes from I think?).