It is best to have log replacement done, but if you have to dig out the rot, apply a liberal amount of borateand fill with wood putty. The wood filler is not cheap either. The problem is that you can seal the rot in and it will continue to degrade the log(s). As for the checks, I do not recommend filling them unless they are over 1/4” wide and are running into a window, door or corner and are allowing wind, water or bugs to enter the home. Filling the checks can also cause log rot if left uninspected for failure on the caulks part.