Does continuous treatment of hypercholesterolemia with statins create any bad effect on your liver?

Usually not. Increased elevations in liver tests may be seen with statin use, but if you're being monitored by your md the. I would not worry about any liver damage.
No. Long term use of statins does not cause liver damage. Historically people have worried about increased liver enzymes on statin therapy. Increased liver enzymes do not indicate liver damage and many patients with elevated enzyme levels can be safely continued on statin therapy. Check with your physician for further discussion.