What happens in the twin paradox if the ship doesn't return? What happens if the twin in the spaceship doesn't return?  Would he still be younger than his other twin?  Is the symmetry broken simply by accelerating out of earth? If it is still symmetrical when he doesn't return, why do satellites have a different time than the time on earth if they didn't return?
 A: What happens if the twin in the spaceship doesn't return? Would he still be younger than his other twin? 
It's really a moot point, because you can't compare clocks. There is no absolute time! You can't say, "What's each twin's age at this instant?" because "this instant" depends on the observer. 
Is the symmetry broken simply by accelerating out of earth?
That and accelerating back. 
If it is still symmetrical when he doesn't return, why do satellites have a different time than the time on earth if they didn't return?
Satellites have a different time than on earth because of weaker gravity. They also experience orbital acceleration which breaks symmetry from us.
A: To keep things simple, let us assume that there is no acceleration outside of the self-propulsion that the rocket ship uses to travel. If the ship returns, the twin who was on it will definitely be younger because of general relativity reasons. However, if the rocket doesn't come back, then from the point when the rocket reaches a constant velocity after first accelerating during take-off to however many years after, both twins are viewed as being in inertial reference frames and general relativity no longer applies.
In this case, if the rocket were to keep going at constant velocity for however many years after that point, and, at the end of those years, you somehow waved a magic wand so that the two twins instantaneously appeared before you, they would appear to you to have both aged the same amount since that point.
