Thanks for quick reply first of all,
So,
1/I attached the screenprint of my Corona Path in User Preferences in Blender.
2/second screenshot presents how the path should look like based on
www.bitbucket.org (from which I downloaded the latest Corona Standalone 3, by the way).
3/ In a mean time I found that, actually Corona works, but only if I open it from outside the Blender each time I tweak some changes in the scene. It is bit annoying.
4/ Material preview doesn't work, although, and I have a trouble with render image textures, Corona crushes.
Whats your suggestions??