1. Good question but we don't know the answer. Actually, let's rephrase it a bit. It doesn't mean anything to 'travel at a speed' because our relativistic world doesn't have any physical speed measuring effects. You can take two objects traveling at some speed with respect to each other and ask if, without either one feeling any acceleration, they end up meeting again. So that's what I take your question to mean. But I still don't know the answer.
The universe is close to 'flat', just in between 'open' and 'closed'. The answer would be yes in a closed universe and no in an open or flat universe. There's no experimental way right now to tell if the universe is just barely closed.
2. When people say the universe may be like a sphere (the surface of a solid ball), they don't mean that the universe is two-dimensional. They mean like the 3-D surface of a 4-D ball. The direction 'into' or 'out of' the sphere has no physical meaning, there's no there there.
3.You're right that relativistic effects don't change how long you would experience life. All
your clocks- your wristwatch, your heart, your thoughts, etc. - proceed in synchrony with each other. What does depend on your path through space-time is how much you get to see of the aging of others. As you say, that can be very different for the two twins. Who knows which one is better off?
(published on 10/22/2007)