To answer your first question, I found my first Book after only a few black kats, during the first Kataclysmic Konfrontation. This experience seems to be far from typical.
There have been many threads over the years, in which players express their frustration at the low odds of finding the Books (and hence some of the most powerful gear in the game). It makes everything too dependent on luck.
There have also been threads where players gather data needed to estimate the Book drop rates. The data sets need to be pretty big to constrain the Book drop rate, because the chances are so low.
If you want to find some of these threads, search Google for something like "black kat book chances site:forums.spiralknights.com" (without the quotation marks).
I have not seen any recent large-scale studies of Book drop rates, so I don't have any reason to believe that the drop rates have changed.
