Water stains are tricky. You should try and sand it out, but if it is too deep you may never sand it out without deforming the log. As for the check (crack), more than likely it is there to stay. Since it is interior, you could fill it with a caulk that matches the color of the log; this is probably the best solution. You could also try to drill some pilot holes and try to pull it shut by running screws into the holes. I doubt it will work though. Maybe replace the log with a new one???