Sure, thanks to the CC developers team, everything is fine so I marked this topic as resolved.
I didn't upgrade the production site on a fly. I set a mirror site with old WP and CC theme versions and then upgraded it. There I spotted a trick how to start a slider working (I mentioned it earlier).
There was a performance issue after I upgraded the production site so I downgraded it. Everything runs smoothly after I upgraded the site again.
My CSS coding wasn't lost after upgrade, I have used Theme Options - CSS - Overwrite CSS.