Hi; This is a good question and that usually means there are no easy answers. Kris's reply is excellent.
It is true we do not understand everything about solar storms (that is why we and many other scientists and engineers are working hard on these questions), and it is true that the Sun may, at some point, produce a solar storm bigger than what we've experienced and there may be some wide spread consequences. It is true that the National Academy of Sciences is aware of this and that awareness has helped direct some of the funding for research.
That all being said, for the most part we DO have enough understanding of the Sun and our immediate galactic surroundings to be able to provide some warning of when the possibility of a huge event may occur. We know what kind of sunspots are generally responsible for huge storms, what kind of solar structures are the precursors to large CMEs, and when those kinds of sunspots and structures are visible, every relevant agency does start watching carefully and acting accordingly. Similarly, the local neighborhood of the galaxy is fairly well mapped out, we are discovering potentially hazardous asteroids all the time and tracking them, and while we don't know everything, what is shown on that site isn't a mysterious Dark Rift, it's a bunch of clouds and dust, mostly Hydrogen, mostly harmless, and mostly not near where we are.
Some other comments about that site: government-issued alerts like are posted there under 'NASA real time solar storm alerts', um, well what is posted is coming from NOAA, not NASA. Without some training, government alerts can sound either boring or worse than they are, and real scientific data is just a bunch of numbers or pictures, and it takes some experience to understand what it all means. So when a site like you found makes things sound scary all the time but you know that in day-to-day life all the scary things aren't happening, the credibility is pretty low ("boy who cried wolf" effect).
There are good sites to help interpret the government alerts, including the same government sites themselves: see The NOAA Space Weather Prediction Center pages http://www.swpc.noaa.gov/primer/primer.html, http://www.swpc.noaa.gov/NOAAscales/index.html for example, of how to interpret some of the NOAA alerts. Seeing a whole bunch of "EXTENDED WARNING: Geomagnetic K-index of 5 expected" can sound alarming, but it helps to understand that it means a minor disturbance, for which the government needs to warn some industries which may see some minor impacts, but won't be noticed and it honestly happens a lot of the time.
What can be cool about some of these real data feeds such as from NOAA or NASA is that with a little bit of education, they can provide for some really cool information about the beautiful aspects of space weather and astronomy, and that merits a lot more attention from everyone than the feat that mis-interpretation brings. The alerts can signal some spectacular aurora, which are the beautiful and wonderous effects. So, a little bit of understanding can bring the fear way down and the interest way back up. There are very few commercial pseudo-science .com sites (vs. commercial research sites, such as where I work or Lockheed, etc) that I'd trust, and again Kris's guidelines are good for trust: watch for spelling errors, bias, un-traceable claims. I'll say most pure research sites are just research and may sound excited about the research but for the most part may also sound dry and boring. From the NOAA Space Weather Prediction Center page, they have trusted links at http://www.swpc.noaa.gov/solar_sites.html. One that Kris mentions, however, that I also really love is spaceweather.com. It is unbiased, filled with very informative commentary, isn't fear-mongering, is filled with great photography, has an atmospheric optics expert on-hand (whose research is easily found and traceable) to explain some weird stuff, and it demonstrates that most of what goes on around us is amazingly cool and interesting and worth watching (rather than being scared of). I strongly suggest to check it out (it's my 'home page").
Cheers, -KD