How fast to travel to end up where i started from? I've heard that if one travels far enough in one direction through the universe, one ends up at the starting point, due to the "geometry" of the universe.
What rate is space expanding at? 
Is it in fact faster than light? 
How fast would one need to travel relative to expanding space/time to end up at the starting point?
 A: Your answer is dependent on many assumption. Your idea of coming back to the starting point was mostly "plausible" before the discovery of dark energy. If the current size and dynamics of spacetime is as we believe as of today, then you will never return back because there will be more space created ahead of you as you travel that what you cover even at the speed of light.
A: I can only think of three ways that you could get back to your starting point by travelling in a straight line:


*

*the universe is closed in the Friedmann sense

*the universe is not simply connected i.e. closed in a topological sense

*the universe as a whole is rotating i.e. it's a Gödel universe
In case 1 there is no special speed to get back to where you started. All trajectories meet at the Big Crunch so you (and everyone else) will get back where you started at the moment of the Big Crunch. There's no way to get where you started faster than this.
An example of case 2 would be if the global topology of space is a 3-torus. If you're interested there is more about this in the Wikipedia article on the shape of the universe. The speed you need to get back to your starting point will depend on the scale at which the universe is closed and the rate of expansion. If this speed were less than the speed of light we'd expect to see some evidence for the topology in observations of distant galaxies. Since we haven't seen anything this suggests that even if the global topology is closed you'd need to travel faster than light to get back to your starting point.
The Gödel universe is an interesting one because it contains closed timelike curves. You could get back not only to the point in space you started from but also the point in time you started from. Sadly there is no evidence that the universe as a whole is rotating, so you can't use this technique to get back where you started.
A: Here's another reason you wouldn't get back to your starting point.  If two people went off in opposite directions at close to the speed of light and returned to the same location, each would observe that the other's clocks were slower and thus would show an earlier time.  (This is different from the twin paradox, in which one twin is accelerating and the other isn't.)  This is a contradiction, and so the universe must be expanding fast enough so that it doesn't happen. 
