The problems you describe sound like inadequate fixation, but in the case
of the second process another problem is removing all of the iron. You
certainly need to replace the fixer very often.
I'm not aware of any problems caused by soft water.
Better results are usually obtained if you use either a gold or a
platinum toner with the second process.
There is a more recent and detailed book on the Kallitype - I can't for
the moment remember the title/author - which would be worth looking at.