From my personal experience I don't think fasting CAUSES stones. However, if you have ANY issues, they will arise at some point while fasting! I passed a kidney calcification during a long fast last summer, but definitely knew my kidneys were acting up before the fast.
Fasting IS a flush... and it flushes liver/gallbladder, kidneys... along with everything else. If you have congestion in any area that is trying to flush it will become painfully apparent.
Sounds like a nice Liver Flush
is a very good idea!