Good answer, a quick correction: even if the math is correct, it doesn't necessarily mean that everything the math predicts has to be real. That's indeed what happened with Dirac, but it doesn't have to be true for all mathematical models of the physical world.

Acceleration is still not the big picture. Only within the framework of special relativity it is true that an acceleration will always result in a shorter length of space time path. When you're talking about acceleration, you are restricted to special relativity only. But the twin paradox can be formulated in general relativity framework as well. In general relativity, you can have situations in which the accelerating twin is older, because in general relativity, even accelerating objects can have longer spacetime lengths...

That's not the paradox. The paradox is that if each twin point of view is relative, then relative to the twin that is on the space ship, it's actually the earth twin that is traveling. So the spaceship twin should be older, not the earth twin. But it's not the case, and this is the paradox.

That's a very good answer. Everyone talks about acceleration all the time, but it's really the length of space time path. For example: you can have a situation in which one twin is in a space ship orbiting earth, and the other twin is in a space ship which is hovering above the surface, canceling gravity with a constant force upwards by its thrusters. In this case, the twin who is moving in orbit will be younger, but he is in constant free fall! It's the twin who hovering which will be older, but he was the one who was subjective constantly to an external force! So it's not acceleration, it's space time length...