I was actually taking a special relativity class when the faster-than-light neutrino thing happened. Class the next day was a bit awkward, but the professor assured us the experiment was as instrumentation error, and he was right, of course.
1. To arrive at point B after -1 sec or backward in time? or
2. To arrive at point B after 0.999 sec from the time he started his journey?
An insane consequence of the theory of relativity is that for assuming you observe 2, there must be a reference frame in which someone else, moving at a constant speed relative to you, observes 1(or something very close). Weird, huh? The fact that you can't move faster than light as a consequence of special relativity is more a demand that effects follow causes. That's probably what the news articles are referencing when they say a particle moving faster than light would need to move backward in time, whether the authors of those news article know it or not. The "relative" in relativity is that time, distance and even simultaneity are all relative, that they depend on your velocity, or, more naturally, your velocity as a fraction of the speed of light. The math behind this is called a Lorentz transformation, and it tells you what an observer who is travelling at a constant velocity relative to you sees. Also, this wiki page explains how both 1 and 2 manifest pretty well.
A few years ago I went to a talk given by Miguel Alcubierre (brag), and someone asked him what he thought about the paradoxes that would be caused by violating causality if his device really were to be built. He kinda just shrugged and said "I guess we'll see what happens" or something like that. It's kind of unknown what would happen even to the experts, and other weird things that happen if something goes faster than the speed of light, too, like space looking like time and time looking like space.
that would pretty much mean that we are stuck in our solar system until the Sun burns up, or until some cosmic explosion wipes us all out.
That isn't necessarily true. DARPA is funding a project to figure out if interstellar travel is feasible and I doubt that they're assuming a method that involves faster-than-light travel. A common idea I've heard proposed in generation ships, ships large enough to support several generations of humans who would go on to colonize a new planet, but that's obviously at least several hundred years away.